Why UDA proves nothing
Pierz
can't accept that it is anything like a 'proof'. I keep reading Bruno
making statements like "If we are machine-emulable, then physics is
necessarily reducible to number psychology", but to me there remain
serious flaws, not in the logic per se, but in the assumptions.
Bruno says that "no science fiction devices are necessary, other than
the robust physical universe". He also claims that to argue that the
universe may not be large or robust enough (by robust I assume he
means stable over time) to support his Universal Dovetailer is "ad
hoc and disgraceful". I think it is anything but. To describe such an
argument as "disgraceful" is to dismiss with a wave of the hand the
entirety of modern cosmology and physics, disciplines which after all
have managed to produce a great deal more results in the way of
prediction, explanation and tangible benefits than Bruno's theory (I
insist it is a theory and not a 'result'). As a computer science
expert, I assume Bruno is aware of modern computational approaches to
physics. Such approaches explicitly forbid any kind of 'infinite
informational resolution' as is required by Bruno's theory. The
information content of the universe is seen as being a fundamental
quantity much like energy, constantly transforming but conserved over
the whole system in the same way energy is. This computational
approach indeed seems to be the *basis* for much of Bruno talks about
(computability, emulability and so on are all fundamental ideas), but
then he flies in the face of it by proposing some kind of automated,
Platonic computation devoid of any constraints in terms of state
memory or time.
Let's take a look at the UD. Obviously this is not an 'intelligent'
device, beyond the intelligence implicit in the very simple base
algorithm. It just runs every possible computer program. Random
computer programs are made of and produce *static*, they are a random
arrangement of bits. Now clearly, we know that if you look at a large
enough field of static, you will find pictures in it, assemblies of
dots that happen to form structured, intelligible images. Likewise in
the field of random computed algorithms, very very occasionally one
will make some kind of 'sense', although the sense will naturally be
entirely accidental and in the vast, vast majority of cases will give
way a moment later to nonsense again. So when the UD runs through its
current sequence of programs, what it is really doing is just
generating a vast random field of bits. Nonetheless, each of these
individual programs needs to have potentially infinite state memory
available to it (the Turing machine tape). Now the list of of programs
run by the machine continues to grow with each iteration as it adds
new algorithms, so it takes longer and longer to return to program 0
to run the next operation. As it needs to run *all* programs, a
necessarily infinite number, it requires infinite time, but for some
reason Bruno thinks this is not important. Either it has infinite
processing speed as well as memory, or it has infinite time on its
hands.
Fine. But then we can simply dispense with the UD altogether and just
gather up its final results, which is an infinite field of static, a
giant digital manuscript typed by infinite monkeys. Everything capable
of being represented by information will exist in this field, which
means it is capable of "explaining" everything. And nothing.
We have to deconstruct the notion of "computation" here. Computation
is the orderly transformation of information. But the UD's orderliness
is the orderliness of the typing monkey. If it is orderly at all, it
is by mistake. By talking about it the UD as performing computation
more intelligence is implicitly imputed than this hypothetical device
possesses. Yes, it would generate every possible information state,
and would therefore create me and all my possible futures, but these
'pictures' would have no coherence, would immediately dissolve back
into the static they emerged from. The UD, as a generator of static,
cannot explain coherence in my experience.
There is a fundamental circularity here. Something must explain the
coherence of 1p and 3p accounts (laws of physics). Because the UD must
exist (someone please explain this to me!), the explanation must lie
in the UD. Because the UD is pure computation, the laws of physics
(the coherence) must be reducible to principles of computation. But
why no earth must the UD exist? And if it did exist, the reduction of
the UD to an infinite static field shows that it is devoid of such
explanatory power. Only if there is something about the UDA that
confines it to meaningful, orderly algorithms (whatever that might
mean), can Bruno's argument follow. But the UD's algorithm is a few
lines of code, there is no hidden magic to allow it to select such
algorithms. We have to throw out the UD, not the laws of physics.
The whole notion of the 'teleporting consciousness' is obviously
fundamental to the argument. It is assumed by 'yes doctor' (and argued
for in step 8) that consciousness is not bound to any physical
substrate, but is a function of certain computational states - ie
arrangements of bits. What again is deeply unclear is how a boundary
is formed around such arrangements to give them coherence in the
overall field. In an infinite field of transforming information - the
output of the UD - there will be areas of apparent coherence, but the
coherence is apparent, not real. Such a coherent region could only be
identified by a mind (or computer) capable of recognizing coherence or
pattern. The UD does not possess such intelligence, or only as yet
another algorithm which is on the same level as the other algorithms,
and not capable of accessing the states of all other computational
threads. You'd need to posit some new level of meta-computation
picking out the coherent results of the UD from the incoherent ones,
but how does *it* recognise coherence? It's an infinite regress.
And how do these coherent areas of the field which we call
consciousnesses (or 1p) connect with their self-similar regions in the
UD output? There may be pictures of me in all possible states within
this field, but they will be completely disconnected from one another.
How does the consciousness apparently implicit in the picture of me
'join the dots' between these random images to make a timeline which
defines my history? The argument that it is 'machine psychology' or
'laws of arithmetic' merely begs the question - or obfuscates it.
In the end, the UDA merely asserts the results of its own assumptions,
but the assumptions are profoundly doubtful. You can dress the
emperor's nakedness up in a lot of fancy mathematical formulism and
obscure verbal manoeuvres, but he is still naked. Infinite randomness
is a 'powerful' explanation because you can find anything you like
inside it. But when you see how vast the sea of surrounding
meaninglessness is, you realise the bankruptcy of that mode of
explanation.
meekerdb
If you are simulating a physical process on a computer, the time the computer takes to
simulate one second of the physical process may be anything. The simulator time and the
simulated time are completely different. The simulated events need not even be produced
in the order of their (simulated) time stamp.
>
> Fine. But then we can simply dispense with the UD altogether and just
> gather up its final results,
It has no final results since in general the programs will not terminate.
> which is an infinite field of static, a
> giant digital manuscript typed by infinite monkeys. Everything capable
> of being represented by information will exist in this field, which
> means it is capable of "explaining" everything. And nothing.
I empathize with that objection. It is easy to produce everything, but what we want is an
explanation for *this* thing. This is known as "the white rabbit problem" or the "measure
problem" since implicitly the idea to explain that there is some natural measure by which
*this* is highly probable and *that*, including Alice's white rabbit, is highly
improbable. The whole problem is pushed off into finding and justifying this measure.
It would not be appropriate to invoke intelligence in the explanation, since part of the
point is to explain intelligence, consciousness, etc. After all there is no assumption
that the equations of physics are "intelligent"; yet they provide a pretty good story of
the origin and development of the universe.
> or only as yet
> another algorithm which is on the same level as the other algorithms,
> and not capable of accessing the states of all other computational
> threads. You'd need to posit some new level of meta-computation
> picking out the coherent results of the UD from the incoherent ones,
> but how does *it* recognise coherence? It's an infinite regress.
"It" doesn't. It is rather that coherence picks out "us". But this is rather like the
Boltzman brain problem. For example if it picks out me according as some measure makes
"me" more probable, why don't I find myself in a world in which everyone is Brent Meeker.
Brent
"A theory that can explain anything, fails to explain at all."
Bruno Marchal
On 25 Sep 2011, at 04:20, Pierz wrote:
> OK, so I've read the UDA and I 'get' it,
Wow. Nice!
> but at the moment I simply
> can't accept that it is anything like a 'proof'.
Hmm... (Then you should not say "I get it", but "I don't get it"). A
proof is only something presented as a proof. You can only say: here
is the flaw, (in case you have found one). I guess that is what you
did, or thought you did.
> I keep reading Bruno
> making statements like "If we are machine-emulable, then physics is
> necessarily reducible to number psychology", but to me there remain
> serious flaws, not in the logic per se, but in the assumptions.
>
> Bruno says that "no science fiction devices are necessary, other than
> the robust physical universe".
To get the step-7. But that robust universe assumption is discharged
in the step 8. Which I have explained with more details (than in
sane04) on this very list:
http://www.nabble.com/MGA-1-td20566948.html#a20566948
> He also claims that to argue that the
> universe may not be large or robust enough (by robust I assume he
> means stable over time) to support his Universal Dovetailer is "ad
> hoc and disgraceful". I think it is anything but.
By robust I mean expanding enough to run the UD.
It is disgraceful with respect to the reasoning. But if for some
reason, you believe that there are evidence that the physical universe
does develop the infinite running of a UD, then you can skip the last
(and most difficult) step 8. Physics is already a branch of computer
science/number theory, in that case.
This is funny: if we have evidence that the physical universe has a
never ending running UD, then we can from step 7 alone conclude that
physics is a branch of number theory. And by Occam, we don't need to
assume the primitive physical universe.
But we don't, and I doubt we can, have such an evidence. The UD
running is very demanding. Not only the universe must expand
infinitely, but in a way which connect solidly all its parts. Better
to grasp the step 8 (the movie graph argument).
> To describe such an
> argument as "disgraceful" is to dismiss with a wave of the hand the
> entirety of modern cosmology and physics, disciplines which after all
> have managed to produce a great deal more results in the way of
> prediction, explanation and tangible benefits than Bruno's theory (I
> insist it is a theory and not a 'result').
Yes, it is the theory known as "mechanism". The theory that the brain
is a natural machine. The result is that physics emerges from
numbers, or combinators, or from any first order specification of a
universal machine, in the sense of theoretical computer science
(branch of math).
> As a computer science
> expert, I assume Bruno is aware of modern computational approaches to
> physics. Such approaches explicitly forbid any kind of 'infinite
> informational resolution' as is required by Bruno's theory.
Where is this required?
Note that as a corollary of UDA we can show that the physical universe
is not a computable object, a priori.
The computational approach to physics can have many interesting
application, but it can't tackle the mind body problem. But to get
this, it is better to grasp UDA first.
> The
> information content of the universe is seen as being a fundamental
> quantity much like energy, constantly transforming but conserved over
> the whole system in the same way energy is.
There is no assumption about the universe in the theory. We assume
only that the brain (or the generalized brain, that is the portion of
observable things needed to be emulated for my consciousness to be
preserved) is Turing emulable.
UDA assumes the existence of brains and doctors, and thus on some
physical reality, but not on a primitive physical reality. At the
start of the UDA, we are neutral on the nature of both mind and
universes.
> This computational
> approach indeed seems to be the *basis* for much of Bruno talks about
> (computability, emulability and so on are all fundamental ideas), but
> then he flies in the face of it by proposing some kind of automated,
> Platonic computation devoid of any constraints in terms of state
> memory or time.
Computation is a mathematical notion, discovered by Post, Turing, etc.
It is based on the notion of state memory, time steps, etc. It is not
base on physical implementation of those notion (unlike engineering).
>
> Let's take a look at the UD. Obviously this is not an 'intelligent'
> device,
You are right. It is very dumb. It is not even Turing universal, and
it computes in the most complex possible way the empty function (it
has no input, it has no output).
> beyond the intelligence implicit in the very simple base
> algorithm. It just runs every possible computer program.
Yes.
> Random
> computer programs are made of and produce *static*, they are a random
> arrangement of bits.
There is no randomness in the work of the UD.
> Now clearly, we know that if you look at a large
> enough field of static, you will find pictures in it, assemblies of
> dots that happen to form structured, intelligible images.
OK. But they are not related by computations. Neither in the first
person views, nor in the third person views.
> Likewise in
> the field of random computed algorithms, very very occasionally one
> will make some kind of 'sense', although the sense will naturally be
> entirely accidental and in the vast, vast majority of cases will give
> way a moment later to nonsense again.
The only randomness which might appear comes from the first person
indterminacy, and the fact that we acnnot know in which computation we
are. This leads to the "white rabbit" problem, but the computation
themselves are not random at all, and the WR problem is basically the
problem to which physics is reduced too, at the conclusion of the
reasoning.
> So when the UD runs through its
> current sequence of programs, what it is really doing is just
> generating a vast random field of bits.
I have not the slightest clue why you say that. It is provably false.
No program can generate randomness in this third person way. The
randomness ¨possible* can only appear from the first person (emulated
in the UD) perspective.
The UD generates, to give an example, the program emulating the
Heisenberg matrix of the Milky Way, at the level of string theory, and
this with 10^(10^(10^(10^(10^9999999))))) digits. Notably. Actually it
does it also with 10^(10^(10^(10^(10^9999999))))) + 1 digits, and
10^(10^(10^(10^(10^9999999))))) + 2 digits, etc.
The point here is that all those running are not random structures. In
fact, there is no randomness at all.
> Nonetheless, each of these
> individual programs needs to have potentially infinite state memory
> available to it (the Turing machine tape). Now the list of of programs
> run by the machine continues to grow with each iteration as it adds
> new algorithms, so it takes longer and longer to return to program 0
> to run the next operation.
Right. Note that such delays are not perceptible for the emulated
observers.
> As it needs to run *all* programs, a
> necessarily infinite number, it requires infinite time, but for some
> reason Bruno thinks this is not important.
It is utterly important.
This why the first person indeterminacy bears on a continuum, despite
the digitalness of all present factors.
You attribute me things which I never say, here. n the contrary, the
fact that the UD never stops is crucial.
> Either it has infinite
> processing speed as well as memory, or it has infinite time on its
> hands.
The UD* (the infinite trace or running of the UD) is part of a tiny
part of arithmetical truth (the sigma_1 arithmetical truth).
Step 8 makes the physical running of the UD irrelevant.
UD and UD* are mathematical notion (indeed arithmetical relations).
>
> Fine. But then we can simply dispense with the UD altogether and just
> gather up its final results,
This does not make any sense. A non stopping program does not output
anything.
> which is an infinite field of static, a
> giant digital manuscript typed by infinite monkeys. Everything capable
> of being represented by information will exist in this field, which
> means it is capable of "explaining" everything. And nothing.
I think you miss the step 3: the first person indeterminacy. I think
you miss also the arithmetical non random dynamic of the UD. You are
confusing an infinite set of information, with an infinite non random
and well defined particular computation.
>
> We have to deconstruct the notion of "computation" here. Computation
> is the orderly transformation of information.
I can agree, although information is more an emerging notion. It is
not used in the definition of computation.
> But the UD's orderliness
> is the orderliness of the typing monkey.
Not at all. It is the orderliness of the computations. Or the
orderliness of the sigma_1 sentences and the logic of their
probability/consistency (as it is made completely transparent in the
AUDA: the translation of the UDA in arithmetic, or in the language of
the Löbian machine).
> If it is orderly at all, it
> is by mistake.
It is 100% orderly.
> By talking about it the UD as performing computation
> more intelligence is implicitly imputed than this hypothetical device
> possesses.
Where? The existence of the UD is already a theorem of Peano
Arithmetic. Robinson arithmetic *is* a UD. You need only the
intelligence for grasping addition and multiplication. The UD has been
implemented:
http://iridia.ulb.ac.be/~marchal/bxlthesis/Volume4CC/4%20GEN%20%26%20DU.pdf
And besides, the physical and psychological (theological,
biological,..) order are brought by the machines from inside the
running of the UD. The UD's intelligence is not needed.
> Yes, it would generate every possible information state,
> and would therefore create me and all my possible futures, but these
> 'pictures' would have no coherence, would immediately dissolve back
> into the static they emerged from.
The point is that IF we are machine, then we have no choice other than
extracting the physical laws from the UD. This is done in the
mathematical part, where, contrary to all expectations (at least by
some of my colleagues at the time) we get already quantum logics.
> The UD, as a generator of static,
> cannot explain coherence in my experience.
You need a theory of knowledge. I use the most classical theory of
knowledge (the one by Theaetetus), and it is enough to cut any easy
conclusion against mechanism.
>
> There is a fundamental circularity here. Something must explain the
> coherence of 1p and 3p accounts (laws of physics).
This is explained by the non triviality of the Theaetetus theory of
knowledge, once we take the incompleteness phenomenon into account to
the study of the first person indeterminacy. You might read the second
part of the sane04 paper. But you have to grasp the UDA first.
> Because the UD must
> exist (someone please explain this to me!),
Step 8 shows that the UD does not need to exist physically. It needs
the same time of existence than the sequence of prime numbers.
> the explanation must lie
> in the UD. Because the UD is pure computation, the laws of physics
> (the coherence) must be reducible to principles of computation.
Right. The explanation is provided by the UD and its internal
observers generated by the computations.
> But
> why no earth must the UD exist?
It does not need to exist physically. You have fail to grasp step 3,
5, 6, 7, and/or 8. I think.
It exist mathematically, and by step 8, this means we have to live
with it.
> And if it did exist, the reduction of
> the UD to an infinite static field shows that it is devoid of such
> explanatory power.
I guess you mean UD*. It is better to keep in mind the difference
between the UD (a finite little program), and UD* the infinite
running, or trace, of the UD.
UD* is NOT an infinite static field. It is a highly structured
mathematical object, and, and this is a key point, it get additional
structure when seen from inside by machines (taking the first person
indeterminacy into account). Indeed, it leads to non trivial notion of
truth, belief, knowledge, observation, feeling, and all this, divided
by two (the communicable/provable part, by the machine), and the non
communicable (non provable by the machine) part. This gives quanta and
qualia. (accepting reasonable axiomatic or near axiomatic definition
of those terms). All this is justified in all detail. tell me
precisely what you miss.
> Only if there is something about the UDA that
> confines it to meaningful, orderly algorithms (whatever that might
> mean), can Bruno's argument follow. But the UD's algorithm is a few
> lines of code, there is no hidden magic to allow it to select such
> algorithms. We have to throw out the UD, not the laws of physics.
We can't no more throw out the UD than we can throw out the prime
numbers.
>
> The whole notion of the 'teleporting consciousness' is obviously
> fundamental to the argument. It is assumed by 'yes doctor' (and argued
> for in step 8) that consciousness is not bound to any physical
> substrate, but is a function of certain computational states - ie
> arrangements of bits. What again is deeply unclear is how a boundary
> is formed around such arrangements to give them coherence in the
> overall field.
That is the result. I am not defending mechanism. Just showing that it
is incompatible with physicalism or even with very weak form of
materialism. I reduce the mind body problem to a purely body problem
in computer science/arithmetic. Then in the second part, I do show a
partial solution; based on the logic of provability by Löbian machine.
I extract the logic of stable observation.
> In an infinite field of transforming information - the
> output of the UD -
What output? The UD has no outputs.
> there will be areas of apparent coherence, but the
> coherence is apparent, not real.
What do you mean by "real"?. Such a notion is preposterous in such a
field. When studying a reasoning, you have to stick on the assumption
in the reasoning.
> Such a coherent region could only be
> identified by a mind (or computer) capable of recognizing coherence or
> pattern. The UD does not possess such intelligence, or only as yet
> another algorithm which is on the same level as the other algorithms,
> and not capable of accessing the states of all other computational
> threads.
By the first person indeterminacy, this is is more subtle than what
you say in that paragraph.
> You'd need to posit some new level of meta-computation
> picking out the coherent results of the UD from the incoherent ones,
> but how does *it* recognise coherence? It's an infinite regress.
No. The observers are any self-aware program run by the UD. They build
the coherence. For physics and feeling, this is studied by adding
explicitly the consistency assumption in the machine beliefs, by using
the modal variant of the logic of self-reference, obtained from
provability (Bp), together with the consistency assumption:
Bp & Dt (observation with probability one)
Bp a Dt & p (feeling).
Dt = consistency = ~Bf (f = "0=1").
It works pretty well. We can do that because G* proves Bp equivalent
to them, but G (the machine) cannot see this, and this is how the set
of all computations get structured by the machines.
This is explained in the second part of the sane04 (and is the main
object of my thesis in computer science).
>
> And how do these coherent areas of the field which we call
> consciousnesses (or 1p) connect with their self-similar regions in the
> UD output?
I guess you mean UD*. The answer of this is given by the first person
statistics.
But you must not see the UD Argument as an attempt to explain the
physical (and psychological) reality, but as an attempt to get a
precise formulation of the mind body problem.
The UDA point is only that IF we are machine, then we HAVE TO derived
the physical laws by a relative statistics on the computations, as
seen by first person machine points of view.
AUDA, the interview of the löbian machines, gives the hint needed to
see that it makes sense, and that it is a "real mathematical problem".
And it gives a partial solution, also (which also provides a
transparent arithmetical interpretation of Plotinus theology, but this
has come well after the defense of the thesis). This has been
published if you want to look at the technics. See my url.
> There may be pictures of me in all possible states within
> this field, but they will be completely disconnected from one another.
You must understand that most version of "you" will be generated by
many (long) computations. All I say, if that if we are machine, then
the laws of physics are given by the relative statistics on those
computations going through your state. Then I succeeded in isolating
the logic of the "probability one", and it already gives a quantum
logic close to the Birkhoff von Neumann one.
> How does the consciousness apparently implicit in the picture of me
> 'join the dots' between these random images to make a timeline which
> defines my history?
It is your brain, which makes this. But there are no random images in
UD*.
> The argument that it is 'machine psychology' or
> 'laws of arithmetic' merely begs the question - or obfuscates it.
Not at all. Once you grasp step 8, you have no other choice than using
'machine's theology' (that is the 8 logics described in the
arithmetical version of the UDA). And that theology is defined in
arithmetical terms.
>
> In the end, the UDA merely asserts the results of its own assumptions,
> but the assumptions are profoundly doubtful.
That might be. But they are not mine. It is the very common assumption
that the brain functions like a machine. It is as old as humanity, I
think. It appears in some old indian and chinese text, in the greek
one, and reappear with Descartes, and then is believed, in his modern
digital form, by virtually all scientists today, with some notable
exception (like Penrose).
I am neutral on this.
> You can dress the
> emperor's nakedness up in a lot of fancy mathematical formulism and
> obscure verbal manoeuvres,
*That* is a verbal manoeuvre. Indeed: this is called an insult.
Please, try to really take the time to study the work, and if you have
any doubt on the validity, ask question. That is what a discussion
list is for.
> but he is still naked. Infinite randomness
> is a 'powerful' explanation because you can find anything you like
> inside it.
I don't use the notion of randomness, and there is no randomness in
the UD*.
> But when you see how vast the sea of surrounding
> meaninglessness is,
I beg your pardon?
> you realise the bankruptcy of that mode of
> explanation.
I expose a problem.
I think you have read the work too much quickly, and your tone makes
me suspect some prejudice at the start.
If you want I can explain the UD proof step by step, so that you
might, who knows, find a real flaw. I think you are confusing the
counting algorithm, with the universal dovetailing algorithm. In term
of theories, you are confusion the theory of succession, with the
theory of succession+addition+multiplication. The second one have rich
notion of internal observers, and of internal logics. But even without
those logics, you should be able to grasp the body problem of the
mechanist theory.
You might also try to avoid the use of authoritative arguments, please.
You seem also to confuse the assumption (digital mechanism: a much
weaker form of computationalism than the one discussed in the
literature) and the conclusion: the *necessity* that physics arise
from addition and multiplication.
Bruno
Craig Weinberg
>
> Let's take a look at the UD. Obviously this is not an 'intelligent'
> device, beyond the intelligence implicit in the very simple base
> algorithm. It just runs every possible computer program. Random
> computer programs are made of and produce *static*, they are a random
> arrangement of bits. Now clearly, we know that if you look at a large
> enough field of static, you will find pictures in it, assemblies of
> dots that happen to form structured, intelligible images.
intelligibility could arise at all in the static without an image
cohering visual awareness to experience that. The bits don't know they
are part of an image, so what would know what constitutes
intelligibility? Our own experience with static or other Rorschach
type patterns suggests that intelligibility is highly individual and
not meaningful as a property of the object. What images do emerge
would not make sense to anything which could not or would not be able
to perceive the same kind of visual phenomena in the same human-
neurological way. If I see a cat in the static, it doesn't mean my dog
sees a cat in the static.
>
> Fine. But then we can simply dispense with the UD altogether and just
> gather up its final results, which is an infinite field of static, a
> giant digital manuscript typed by infinite monkeys. Everything capable
> of being represented by information will exist in this field, which
> means it is capable of "explaining" everything. And nothing.
represented by information' is itself a theoretical idea which doesn't
play out in practice, not just because of physical constraints (due to
exponential growth in computation resource requirements) in a finite
material universe, but because our assumptions about what
'information' actually is are unfounded.
>
> We have to deconstruct the notion of "computation" here. Computation
> is the orderly transformation of information. But the UD's orderliness
> is the orderliness of the typing monkey. If it is orderly at all, it
> is by mistake. By talking about it the UD as performing computation
> more intelligence is implicitly imputed than this hypothetical device
> possesses. Yes, it would generate every possible information state,
> and would therefore create me and all my possible futures, but these
> 'pictures' would have no coherence, would immediately dissolve back
> into the static they emerged from. The UD, as a generator of static,
> cannot explain coherence in my experience.
signifying digital data is not automatically a human perception or
experience of that data.
>
> There is a fundamental circularity here. Something must explain the
> coherence of 1p and 3p accounts (laws of physics). Because the UD must
> exist (someone please explain this to me!), the explanation must lie
> in the UD. Because the UD is pure computation, the laws of physics
> (the coherence) must be reducible to principles of computation. But
> why no earth must the UD exist? And if it did exist, the reduction of
> the UD to an infinite static field shows that it is devoid of such
> explanatory power. Only if there is something about the UDA that
> confines it to meaningful, orderly algorithms (whatever that might
> mean), can Bruno's argument follow. But the UD's algorithm is a few
> lines of code, there is no hidden magic to allow it to select such
> algorithms. We have to throw out the UD, not the laws of physics.
although both the principles of computation and physics together with
1-p accounts could be used to triangulate the properties of sense.
>
> And how do these coherent areas of the field which we call
> consciousnesses (or 1p) connect with their self-similar regions in the
> UD output? There may be pictures of me in all possible states within
> this field, but they will be completely disconnected from one another.
> How does the consciousness apparently implicit in the picture of me
> 'join the dots' between these random images to make a timeline which
> defines my history? The argument that it is 'machine psychology' or
> 'laws of arithmetic' merely begs the question - or obfuscates it.
>
that this dot joining can only be possible if the dots are already
joined 'to begin with' but that they are existentially discontinuous
through the involution of time into energy and space into matter. This
is how we are able to make sense of anything - pulling 'wholes through
the holes' so to speak, as we might pinch closed the gaps between dots
on a printed halftone image or pointillist painting, bitmap image, in
our ocular blind spot, etc. This is how 1-p experience works. Not
adding together meaningless machine statements to build toward
meaning, but from beginning with everything and masking or sculpting
out all that is not phenomenologically local to 'I'.
> In the end, the UDA merely asserts the results of its own assumptions,
> but the assumptions are profoundly doubtful. You can dress the
> emperor's nakedness up in a lot of fancy mathematical formulism and
> obscure verbal manoeuvres, but he is still naked. Infinite randomness
> is a 'powerful' explanation because you can find anything you like
> inside it. But when you see how vast the sea of surrounding
> meaninglessness is, you realise the bankruptcy of that mode of
> explanation.
the worldview which we have inherited form the tradition of far-
Occidental abstraction, but I think that worldview fails when applied
to consciousness and life, as it takes for granted all of the sense
that it presumes to make sense of, and leaves only the empty syntactic
trappings as presumptive originators.
Craig
meekerdb
>> Yes, it would generate every possible information state,
>> and would therefore create me and all my possible futures, but these
>> 'pictures' would have no coherence, would immediately dissolve back
>> into the static they emerged from.
>
> The point is that IF we are machine, then we have no choice other than extracting the
> physical laws from the UD.
Actually I think we do. If what you write above is correct then you could infer a
contradiction from assuming a primitive physics - but it seems you discard it as an
application of Occam's razor, not as a contradictory concept. Do you think you can prove
a contradiction from assuming ur-matter? It seems to me that Peter Jones has given a
convincing defense of that as a possible theory of the world.
> This is done in the mathematical part, where, contrary to all expectations (at least by
> some of my colleagues at the time) we get already quantum logics.
>
>
>
>> The UD, as a generator of static,
>> cannot explain coherence in my experience.
>
> You need a theory of knowledge. I use the most classical theory of knowledge (the one by
> Theaetetus), and it is enough to cut any easy conclusion against mechanism.
This is unclear to me. You use Bp & p to denote "knowing p" where p is some proposition.
But it seems that "B" is equivocally "Believes" and "Proves" (Beweisbar). I don't see
that these two are identical.
Brent
Pierz
have offended you. Call it a rhetorical flourish! I apologise. There
are clearly some theories which require a profound amount of dedicated
learning to understand - such as QFT. I majored in History and
Philosophy of Science and work as a programmer and a writer. I am not
a mathematician - the furthest I took it was first year uni, and I
couldn't integrate to save myself any more. Therefore if the truth of
an argument lies deep within a difficult mathematical proof, chances
are I won't be able to reach it. Then my ignorance would hardly
constitute a criticism, and so it may be with UDA and my complaint of
obscurity. On the other hand, it seems to me that ideas about the core
nature of reality can and should be presented in the clearest, most
intelligible language possible. I can't solve QFT equations, but I can
grasp the fundamental ideas of the uncertainty principle, non-
locality, wave-particle duality, decoherence and so on. I'm not
arguing for dumbed-down philosophy, but maximal clarity. Having said
that, I'm prepared to put effort in to learn something new if I have
misunderstood something.
You have misread my tone if you think it indicates bias against your
theory. I have read your paper (at least the UDA part, not the machine
interview) several times, carefully, and presented it to my (informal)
philosophy group, because I certainly find it intriguing. I'll admit
that step 8 is where I struggle - it's not well explained in the paper
yet contains the all the really sweeping and startling assertions. The
argument about passive devices activated by counterfactual changes in
the environment is opaque to me and seems devious - probably defeated
in the details of implementation like Maxwell's demon - but that is
obviously not a rebuttal. I will take a look at the additional
information you've linked to.
I can see that you are actually right in asserting that the UDA's
computations are not random, but I'm not sure that negates the core of
my objection. Actually what the UDA does is produce a bit field
containing every possible arrangement of bits. Is this not correct? I
am open to contradiction on this. If it doesn't, then it means it has
to be incapable of producing certain patterns of bits, but in
principle every possible pattern of bits must be able to be generated.
Now a machine with infinite processing power and infinite state memory
that merely generates random bit sequences would eventually also
generate every possible arrangement of bits. So the UDA and the
ultimate random generator are indistinguishable AFAICS.
I think what you are saying is that somehow this computation produces
more pattern and order than a program which simply generates all
possible arrangements of bits. Why? If I were to select at random some
algorithm from the set of all possible algorithms, it would be pretty
much noise almost all the time. *Proving* it is noise is of course
impossible, because meaning is a function of context. You've selected
out "the program emulating the Heisenberg matrix of the Milky Way",
but among all the other possible procedures will be a zillion more
that perform this operation, but also add in various other quantities
and computations that render the results useless from a physicist's
point of view. There are certainly all kinds of amazing procedures and
unfound discoveries lying deep in the UDA's repertoire of algorithms,
but only when we intelligently derive an equation by some other means
(measurements, theory, revision, testing etc) can we find out which
ones are signal and which ones noise.
>> Fine. But then we can simply dispense with the UD altogether and just
>> gather up its final results,
>This does not make any sense. A non stopping program does not output
>anything.
shorthand for what I was trying to say - didn't have time for an
amendment. By 'results' I mean the machine's state. It seems that for
the UDA to work, we have to assume that the simulation has 'finished',
even though from a 3p perspective it never can. What I mean is, if the
UDA had just started running, it wouldn't have any complex
representations in its trace yet. And since the UDA exists purely
mathematically, platonically, how can it be subject to time at all? It
has no processing limitations, so any notion of time as a factor can
be disregarded. Otherwise you'd have to say that to process an
instruction takes t amount of time, and where would such a constant
come from? The time taken to compute something in the physical world
is a function of the fact that all computation we know of is bound to
the manipulation of physical substrates that are embedded in the
constraints of time, space and energy. Sequentiality in the UDA is
purely conceptual. And because my 1-p moments could be anywhere in
the UD's record of histories, I can't speak about where the UD is up
to in its work 'now', but just have to take it as all somehow 'done',
even though it can 'never' be done. I'm granting this, even though it
is itself problematic. 'Results' was my clumsy shorthand for the UD's
infinite record of states.
If this is a misunderstanding, I'm sure you'll point it out!
Actually I'm not sure why you have to resort to the dovetailing in the
first place. Since you grant your machine infinite computational
resources, why not grant it parallelism? Just to make it a Turing
machine? The Turing machine is just an idea, there's no reason to
think the universe (whatever the hell that is) has to be serial in its
workings.
> The existence of the UD is already a theorem of Peano
> Arithmetic.Robinson arithmetic *is* a UD.
arithmetic is a product of human intelligence. Just because someone
has mentally constructed a mathematics with the structure of the UD
does not instantiate a UD that actually 'runs' and creates the whole
universe! That is a vast mathematical hubris - akin to the way any
person tends to over-apply their dominant metaphors. As a writer it's
very easy to see the universe as a vast story. As a programmer, I see
algorithms everywhere. But I'm not so inflated as to think it's more
than a metaphor. I can invent my own logically consistent set of
axioms right here and now, but I wouldn't presume it was anything more
than a set of mental relations.
Oh, and :
>is the flaw, (in case you have found one). I guess that is what you
>did, or thought you did.
Unfortunately I don't have time to continue my response/questions now
- I'm amazed and impressed you can find the time for such detailed
responses to random ignorants such as me! I'm more than prepared to
concede my naivete and have my eyes opened to the revelation of UDA.
On the other hand, the intelligent naive person has some advantages
(hence the emperor's clothes reference). Whether I'm the child in the
story or merely ignorant is the question. I remain open the
discovering the latter.
> And besides, the physical and psychological (theological,
> biological,..) order are brought by the machines from inside the
> running of the UD. The UD's intelligence is not needed.
>
>
>
>
>
>
>
> > Yes, it would generate every possible information state,
>
> read more »
Bruno Marchal
On 26 Sep 2011, at 01:08, meekerdb wrote:
> On 9/25/2011 10:20 AM, Bruno Marchal wrote:
>>> Yes, it would generate every possible information state,
>>> and would therefore create me and all my possible futures, but these
>>> 'pictures' would have no coherence, would immediately dissolve back
>>> into the static they emerged from.
>>
>> The point is that IF we are machine, then we have no choice other
>> than extracting the physical laws from the UD.
>
> Actually I think we do. If what you write above is correct then you
> could infer a contradiction from assuming a primitive physics - but
> it seems you discard it as an application of Occam's razor, not as a
> contradictory concept. Do you think you can prove a contradiction
> from assuming ur-matter?
I obtain an epistemological contradiction. You can still imagine that
there is some matter, but it can't be related at all to your
consciousness, so it is exactly like invisible horse (except that such
invisible horse can be defined, and primitive matter is never
defined). Such a matter has nothing to do with anything we observe.
That is the point. We already reach it with just the seven first step,
with a strong use of Occam razor. The step 8 just eliminates that
strong use, for the weak use equivalent with the "invisible horse".
> It seems to me that Peter Jones has given a convincing defense of
> that as a possible theory of the world.
I have criticized in detail. You can search my reply to Jones, and
criticize it.
>
>> This is done in the mathematical part, where, contrary to all
>> expectations (at least by some of my colleagues at the time) we get
>> already quantum logics.
>>
>>
>>
>>> The UD, as a generator of static,
>>> cannot explain coherence in my experience.
>>
>> You need a theory of knowledge. I use the most classical theory of
>> knowledge (the one by Theaetetus), and it is enough to cut any easy
>> conclusion against mechanism.
>
> This is unclear to me. You use Bp & p to denote "knowing p" where p
> is some proposition. But it seems that "B" is equivocally
> "Believes" and "Proves" (Beweisbar). I don't see that these two are
> identical.
B = provable = rationally believable. What I say works for any belief
notion for a machine (or a Recursively enumerable set of sentences)
close for the modus ponens rules, and arithmetically sound. That is
what I call the ideally self-referentially correct machine. They are
example of what I call Löbian machines. To extract physics, it would
be useless to interview inconsistent or unsound machines.
Bruno
Jason Resch
I can see that you are actually right in asserting that the UDA's
computations are not random, but I'm not sure that negates the core of
my objection. Actually what the UDA does is produce a bit field
containing every possible arrangement of bits. Is this not correct?
I think you are confusing a bit pattern for a computation. A hard drive can contain any possible bit pattern that will fit on its platter, but this bit pattern won't contain consciousness.
Conversely, if the computer is powered up and running the appropriate program, that program may be conscious. This is the difference between the UD, and the series of integers or the digits of Pi. The UD executes all possible programs, the set of Integers is equivalent to all possible bit patterns.
I think what you are saying is that somehow this computation produces
more pattern and order than a program which simply generates all
possible arrangements of bits. Why? If I were to select at random some
algorithm from the set of all possible algorithms, it would be pretty
much noise almost all the time.
I think you could say the program may be uninteresting, or not contain a mind or minds.
Are you familiar with the Anthropic principle? The idea that observers will always find themselves in places where they can exist. They perform the selection by virtue of their existence and observation of their environment.
The vast majority of programs may not contain observers, but those few that do will become environments for the minds they host.
*Proving* it is noise is of course
impossible, because meaning is a function of context. You've selected
out "the program emulating the Heisenberg matrix of the Milky Way",
but among all the other possible procedures will be a zillion more
that perform this operation, but also add in various other quantities
and computations that render the results useless from a physicist's
point of view. There are certainly all kinds of amazing procedures and
unfound discoveries lying deep in the UDA's repertoire of algorithms,
but only when we intelligently derive an equation by some other means
(measurements, theory, revision, testing etc) can we find out which
ones are signal and which ones noise.
We can ignore the computations which don't contain observers, and as far as predicting your own future, we can ignore those that don't contain you.
You also asked about why not execute them all in parallel. Every program does exist in math independetly of the UD. I think the reason Bruno described the UD was that it was a simple single program he could show exists in math. You also questioned whether the existence of the UD is something really there or some mental construction of ours. If you think "17 is prime" is true independently of your knowledge of it, then the statement "the UD does not halt" is also true independently of your knowledge of it.
Jason
Stephen P. King
I really would like to understand how it is that the truth valuation of a proposition is not dependent on our knowledge of it can be used to affirm the meaning of the referent of that proposition independent of us? How does the sentence "17 is prime is a true statement" confer implicit meaning to its referent?
Onward!
Stephen
Jason Resch
That sentence was hard to parse! If I understand it correctly, you are asking how a truth, independent of our knowledge, can confer meaning to something without us?
Things unknown to anyone can have consequences which are eventually do make a difference to beings which are aware of the difference. A comet colliding with the Earth and hitting a pond of unicellular organisms may have drastically altered the course of evolution on our planet. That such a comet impact ocurred is a fact which is either true or false, despite it being independent of anyone's knowledge of it. Yet it has perceptable results.
Correspondingly, the existence of some mathematical truth (even if not comprehended by anyone) can have effects for observers, in fact, it might explain both the observers themselves and their experiences.
How does the sentence "17 is prime is a true statement" confer implicit meaning to its referent?
What is the referent in this case? 17? And what do you mean by "meaning"? 17's primality is a fact of nature. The statement's existence or non-existence, comprehension or non-comprehension makes no difference to 17, only what you could say we humans have discovered about 17.
Jason
Bruno Marchal
On 26 Sep 2011, at 04:42, Pierz wrote:
> OK, well first of all let me retract any ad hominem remarks that may
> have offended you. Call it a rhetorical flourish! I apologise. There
> are clearly some theories which require a profound amount of dedicated
> learning to understand - such as QFT. I majored in History and
> Philosophy of Science and work as a programmer and a writer. I am not
> a mathematician - the furthest I took it was first year uni, and I
> couldn't integrate to save myself any more. Therefore if the truth of
> an argument lies deep within a difficult mathematical proof, chances
> are I won't be able to reach it.
That is the reason why I separate UDA from AUDA. Normally UDA can be
understood without much math, which does not mean that it is simple,
especially the step 8. (but the first seven step shows already the big
picture).
AUDA, unfortunately, needs a familiarity with logic, which
unfortunately is rather rare (only professional logicians seems to
have it).
> Then my ignorance would hardly
> constitute a criticism, and so it may be with UDA and my complaint of
> obscurity.
When I teach orally UDA. The first seven step are easily understood.
This contains most of the key result (indeterminacy, non-locality, non
cloning theorem, and the reversal physics/theology (say) in case the
universe is robust.
The step 8 is intrinsicaly difficult, and can be done before. A long
time ago, I always presented first the "step 8" (the movie graph
argument) and then the UDA1-7.
I am still not entirely satisfied myself by the step 8 pedagogy.
> On the other hand, it seems to me that ideas about the core
> nature of reality can and should be presented in the clearest, most
> intelligible language possible.
I have 700 pages version, 300 pages version, 120 pages version, up to
sane04 which about a 20 pages version. The long version have been
ordered to me by french people, and are written in french.
The interdisciplinary nature of the subject makes it difficult to
satisfied everybody. What is simple for a logician is terribly
difficult for a physicist. What is obvious for philosphers of mind,
can make no sense for a logician or a physicist, what is taken granted
by physicists are total enigma for logicians, etc.
> I can't solve QFT equations, but I can
> grasp the fundamental ideas of the uncertainty principle, non-
> locality, wave-particle duality, decoherence and so on. I'm not
> arguing for dumbed-down philosophy, but maximal clarity.
OK. Note that my work has been peer reviewed, and is considered by
many as being too much clear, which is a problem in a field (theology)
which is still taboo (for some christian, and especially the atheist
version of christianism). I can appear clear only to people capable of
acknowledging that science has not yet decided between Aristotle and
Plato reality view. So when I am clear, I can look too much
provocative for some.
> Having said
> that, I'm prepared to put effort in to learn something new if I have
> misunderstood something.
OK. Nice attitude.
>
> You have misread my tone if you think it indicates bias against your
> theory. I have read your paper (at least the UDA part, not the machine
> interview) several times, carefully, and presented it to my (informal)
> philosophy group, because I certainly find it intriguing.
OK. Nice.
> I'll admit
> that step 8 is where I struggle
Hmm, from your post, it seemed to me that there remains some problem
in UDA1-7.
> - it's not well explained in the paper
> yet contains the all the really sweeping and startling assertions.
When I presented UDA at the ASSC meeting of 1995 (I think) a "famous"
philosopher of mind left the room at step 3 (the duplication step). He
pretended that we feel to be at both places at once after a self-
duplication experience. It was the first time someone told me this. I
don't know if he was sincere. It looks some people want to believe UDA
wrong, and are able to dismiss any step.
> The
> argument about passive devices activated by counterfactual changes in
> the environment is opaque to me and seems devious - probably defeated
> in the details of implementation like Maxwell's demon - but that is
> obviously not a rebuttal. I will take a look at the additional
> information you've linked to.
OK. Maudlin has found a very close argument. Mine is simpler (and
older).
>
> I can see that you are actually right in asserting that the UDA's
> computations are not random,
OK.
> but I'm not sure that negates the core of
> my objection. Actually what the UDA does is produce a bit field
> containing every possible arrangement of bits. Is this not correct?
It generates old inputs of all programs, including infinite streams.
Those can be considered as random. But what the program does with such
input is not random.
> I
> am open to contradiction on this. If it doesn't, then it means it has
> to be incapable of producing certain patterns of bits, but in
> principle every possible pattern of bits must be able to be generated.
As inputs, yes. As computation? No.
> Now a machine with infinite processing power and infinite state memory
> that merely generates random bit sequences would eventually also
> generate every possible arrangement of bits. So the UDA and the
> ultimate random generator are indistinguishable AFAICS.
Not really. In fact the random inputs might play a role in making
possible to have a measure on the computational histories. It can
entail also that the "winning computations" (= those being normal in
the Gaussian sense) inherit a random background, which would make
other feature of the usual (quantum) physics confirming comp. Everett
QM makes such a random background unavoidable in any normal branch of
the universe, like when we send a sheaf of electron prepared in the
state (1/sqrt(2)(up + down), on a device measuring them in the {up,
down} base. This should not be a problem, and if it proved to be an
insuperable problem, then comp is refuted. I have no problem with
that, given that my goal consists in showing that comp is "scientific"
in the popperian sense (refutable).
>
> I think what you are saying is that somehow this computation produces
> more pattern and order than a program which simply generates all
> possible arrangements of bits. Why? If I were to select at random some
> algorithm from the set of all possible algorithms, it would be pretty
> much noise almost all the time. *Proving* it is noise is of course
> impossible, because meaning is a function of context. You've selected
> out "the program emulating the Heisenberg matrix of the Milky Way",
> but among all the other possible procedures will be a zillion more
> that perform this operation, but also add in various other quantities
> and computations that render the results useless from a physicist's
> point of view. There are certainly all kinds of amazing procedures and
> unfound discoveries lying deep in the UDA's repertoire of algorithms,
> but only when we intelligently derive an equation by some other means
> (measurements, theory, revision, testing etc) can we find out which
> ones are signal and which ones noise.
Suppose that you are currently in state S (which exist by the comp
assumption). The UD generates an infinity of computations going
through that state. All what I say is that your future is determined
by all those computations, and your self-referential abilities. If
from this you can prove that your future is more random than the one
observed, then you are beginning to refute rigorously comp. But the
math part shows that this is not easy to do. In fact the random inputs
confer stability for the programs which exploits that randomness, and
again, this is the case for some formulation (à-la Feynman) of QM.
>
>>> Fine. But then we can simply dispense with the UD altogether and
>>> just
>>> gather up its final results,
>
>> This does not make any sense. A non stopping program does not output
>> anything.
>
> OK. I realised after I posted that this was wrong, actually hasty
> shorthand for what I was trying to say - didn't have time for an
> amendment. By 'results' I mean the machine's state. It seems that for
> the UDA to work, we have to assume that the simulation has 'finished',
> even though from a 3p perspective it never can.
I don't think so. The terminating computation are on the contrary rare
compared to the non terminating, and so might have a null measure. To
"appear" in the UD*, all we need is that some program go through your
state, not that a program has to stop on that state, or output that
state.
> What I mean is, if the
> UDA had just started running, it wouldn't have any complex
> representations in its trace yet. And since the UDA exists purely
> mathematically, platonically, how can it be subject to time at all?
The UD generate all "times" in relation with its own internal time,
which can be defined by the steps of its own computation.
This gives a block mindscape, no more threatening subjective time or
physical time than any physicalist bloc-universe conception of
reality, which in physics is already necessary with special relativity.
> It
> has no processing limitations, so any notion of time as a factor can
> be disregarded. Otherwise you'd have to say that to process an
> instruction takes t amount of time, and where would such a constant
> come from?
Just imagine the trace of the UD.
You have many notion of time.
The most basic one is given, as I said, by the number of step of the
UD itself.
Then, for each program generated, you can take the number of steps of
that particular program. Those are sub-step of the preceding one. If a
self-aware creature appears on that particular computation, he will
not be aware of the UD step, but might be aware of the step of "its
own" program.
There many other times notion. The subjective time (à-la Bergson) is
recovered by the logic of knowledge of the self-aware entity
themselves, and handled by the logic of self-reference.
> The time taken to compute something in the physical world
> is a function of the fact that all computation we know of is bound to
> the manipulation of physical substrates that are embedded in the
> constraints of time, space and energy. Sequentiality in the UDA is
> purely conceptual.
Perhaps, but it is better to remain neutral about the primary or not
nature of the physical time. No physical theories is assumed, beyond
the fact that we need some physical reality (but not necessarily a
primitive one). If not, you beg the question.
> And because my 1-p moments could be anywhere in
> the UD's record of histories, I can't speak about where the UD is up
> to in its work 'now', but just have to take it as all somehow 'done',
Right. And you next 1p moment, results from the statistical
indeterminacy in UD*.
> even though it can 'never' be done. I'm granting this, even though it
> is itself problematic. 'Results' was my clumsy shorthand for the UD's
> infinite record of states.
OK.
>
> If this is a misunderstanding, I'm sure you'll point it out!
It is correct, but the states are connected. From the 3p description
of each computation, they are connected by the program leading to such
computation. From the 1-p views, it is quite different, they are
connected by all programs leading to such states. It is a bit like
there is a competition among infinities of (universal) programs for
defining your private 1p history.
>
> Actually I'm not sure why you have to resort to the dovetailing in the
> first place. Since you grant your machine infinite computational
> resources, why not grant it parallelism? Just to make it a Turing
> machine? The Turing machine is just an idea, there's no reason to
> think the universe (whatever the hell that is) has to be serial in its
> workings.
The UD is not the universe. To be sure, there is no physical primary
universe at all (unless some number conspiracy is at play, which
cannot be entirely excluded, but this would mean my brain is the
physical universe, which I doubt). Physical reality is defined by the
way infinitely many computations define normal and lawful shared
"dreams".
Dovetailing assure that the set of all computations is a well define
effective set. Parallelism is defined from this. If I postulate
parallelism, this will be difficult, and ambiguous. The work relies on
Church thesis, for making "universal" mathematically and precisely
definable.
>
>> The existence of the UD is already a theorem of Peano
>> Arithmetic.Robinson arithmetic *is* a UD.
>
> Huh? You've inverted ontological priority completely. Any form of
> arithmetic is a product of human intelligence.
For a logician, a theory is just a number, relatively to another
number. They exist independently of us, like the number 17 exists
independently of us. Human wiill use richer alphabet, but
axiomatizable theories are really machine or program, or recursively
enumerable set (this can been made precise by a theorem of Craig).
In AUDA I use Robinson arithmetic as defining the basic ontology. It
is just a logician rendering of a sigma_1 complete theory/machine,
that is a Turing universal machine. Then, the more richer theories
(like the infinitely richer Löbian observers) are simulated by
Robinson arithmetic. That is a particularity of comp: the ontology is
much less rich than the epistemology on the internal observer, like
the UD is dumber than an infinity of the programs that it will run.
> Just because someone
> has mentally constructed a mathematics with the structure of the UD
> does not instantiate a UD that actually 'runs' and creates the whole
> universe!
The expression "whole universe" is ambiguous, and far more complex to
define than the elementary arithmetical truth needed.
Also, we should better be agnostic on the primary existence of that
universe. Its primary existence is not a scientific fact.
All you need to "believe", to give sense to the comp hyp. is that
elementary arithmetical truth are not dependent of humans.
In case you believe that, "17 is prime" does depend on humans, then I
will ask you to define human, and to explain me the dependence in a
theory which does not assume its independence. Actually, logicians
have proved that this is not possible. Elementary arithmetic, or
equivalent, have to be postulated.
> That is a vast mathematical hubris - akin to the way any
> person tends to over-apply their dominant metaphors. As a writer it's
> very easy to see the universe as a vast story.
Comp implies that the phsyical reality will appear to be deep (very
long, perhaps infinitely long) from the internal observers point of
view. To stabilize sharable computations, we need deep computation (in
the Bennett sense of deep), and linearity at the botton, which has
already been isolated from self-reference logics (I skip the nuance
for not being too much long and technical).
> As a programmer, I see
> algorithms everywhere. But I'm not so inflated as to think it's more
> than a metaphor.
The key point here, is that if you say "yes to a doctor", he will put
in your skull a computer, and this, in case you survive (the comp
case) is not a metaphor.
If you want, no digital machine can distinguish a mathematical reality
from a primary physical one. And the mathematical definition of
reality by physicist are also given by particular universal machine.
Who run those machine. Comp gives an answer: they are run by the laws
of addition or multiplication of numbers, or by the laws of
abstraction and application of lambda term. Eventually, physics is
shown to not depend on the choice of the initial universal system. In
a sense, physics is treachery: it postulate the simplest universal
machine that we observe. But comp explain that the physical universe
cannot be such a machine, and that if we want to extract both qualia
and quanta, we have to derived the physical laws from any universal
machine.
> I can invent my own logically consistent set of
> axioms right here and now, but I wouldn't presume it was anything more
> than a set of mental relations.
Don't take the mental granted. Don't take the physical granted.
>
> Oh, and :
>> A proof is only something presented as a proof. You can only say:
>> here
>> is the flaw, (in case you have found one). I guess that is what you
>> did, or thought you did.
>
> That's kind of pedantic. You know what I'm doing.
>
> Unfortunately I don't have time to continue my response/questions now
> - I'm amazed and impressed you can find the time for such detailed
> responses to random ignorants such as me!
If ever you understand AUDA, you will understand that UDA is
understandable by any Löbian universal machine.
The only problem with the "old" humans, is that they are not always
aware of their millenary assumption/prejudices, especially when they
are experts, curiously enough. I like to share my questioning with
people having a personal sincere interest.
> I'm more than prepared to
> concede my naivete and have my eyes opened to the revelation of UDA.
Lol. You can follow UDA on the entheogen forum. Ah but I see you just
send a post there too. Good. Ask there, because I don't want to bore
too much the people of the everything list with a nth explanation of
UDA. Unless other insist, I prefer to link people to the UDA treads of
the entheogen forum.
> On the other hand, the intelligent naive person has some advantages
> (hence the emperor's clothes reference).
Some universities (not all, not all departments 'course) are often as
much rotten than some political government. The diploma sometimes
measure only the ability to lick the shoes of bosses, and in the right
order, please. Human are still driven by the gene: "the boss is
right". Useful in war, and in hard life competition, but a bullet for
free exploration.
Layman have often a more genuine interest, and they are less blinded
by their expertise, and narrow specialities. We live a sad period for
knowledge, education, science, and even art. The "publish or perish"
dicto has transformed some researcher into cut and paste machine,
searching only funding and nothing else.
> Whether I'm the child in the
> story or merely ignorant is the question. I remain open the
> discovering the latter.
It is up to you,
Bruno
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>
Stephen P. King
Essentially, yes.
Things unknown to anyone can have consequences which are eventually do make a difference to beings which are aware of the difference. A comet colliding with the Earth and hitting a pond of unicellular organisms may have drastically altered the course of evolution on our planet. That such a comet impact ocurred is a fact which is either true or false, despite it being independent of anyone's knowledge of it. Yet it has perceptable results.
The web of causes and effects is an aspect of the material universe. I am taking that concept into consideration.
Correspondingly, the existence of some mathematical truth (even if not comprehended by anyone) can have effects for observers, in fact, it might explain both the observers themselves and their experiences.
Slow down! "existence of some mathematical truth"??? Do you mean the truth value of some existing mathematical statement? That is what I mean in my question by the phrase "truth valuation of a proposition". Is a truth value something that exists or does not exist?
How does the sentence "17 is prime is a true statement" confer implicit meaning to its referent?
What is the referent in this case? 17? And what do you mean by "meaning"? 17's primality is a fact of nature. The statement's existence or non-existence, comprehension or non-comprehension makes no difference to 17, only what you could say we humans have discovered about 17.
Is the symbol 17 the same extant as the abstract number it refers to? Do you believe that symbols and what they represent are one and the same thing??? How does not the fact that many symbols can represent one and the same extant disprove this hypothesis? Is the word "tree" have a brownish trunk and greenish foliage? What about the case where sets of symbols that have more than one possible referent? Consider the word FORD. Does it have wheels and a motor? What is the height of the water that one displaces when we might walk across it? There is a categorical difference between an object and its representations and the fact that one subobject of those categories exists is not proof that a subobject in another category has a given truth value. BTW, truth values are not confined to {True, False}.
Onward!
Stephen
Jason
meekerdb
> Suppose that you are currently in state S (which exist by the comp assumption).
But what does "you" refer to? The comp assumption seems ambiguous. Is it the assumption
that "you" are instantiated by a specific computation? Or is it the assumption that your
brain could be replaced, without you noticing, by a physically different computer, so long
as it computed the same function (at some level). These seem slightly different to me and
are only identical if QM is false and the world is strictly classical and deterministic.
At a practical level the brain is certainly mostly classical and so I might say 'yes' to
the doctor even though my artificial brain will have slightly different behavoir because
it has different counterfactual quantum behavior. But this difference seems to present a
problem when trying to identify "you" within the inifinite bundle of computations
instantiating a particular state in the UD computations.
Of course if you replace the whole universe with an emulation, instead of just my brain,
then my emulated brain in the emulated universe can have the same behavior as my natural
brain in this universe.
> The UD generates an infinity of computations going through that state. All what I say is
> that your future is determined by all those computations, and your self-referential
> abilities. If from this you can prove that your future is more random than the one
> observed, then you are beginning to refute rigorously comp. But the math part shows that
> this is not easy to do. In fact the random inputs confer stability for the programs
> which exploits that randomness, and again, this is the case for some formulation (�-la
> Feynman) of QM.
How is this?
Brent
Jason Resch
I am not sure what you mean by "exists" in this case so let me say this, the state of being true, or the state of being false, for the proposition in question, was settled before a human made a determination regarding that proposition.
[SPK]
How does the sentence "17 is prime is a true statement" confer implicit meaning to its referent?
What is the referent in this case? 17? And what do you mean by "meaning"? 17's primality is a fact of nature. The statement's existence or non-existence, comprehension or non-comprehension makes no difference to 17, only what you could say we humans have discovered about 17.
Is the symbol 17 the same extant as the abstract number it refers to?
No, as I mentioned to Brent in a post the other day, we ought not confuse the label for the thing. Nor should we confuse our idea of a thing for the thing itself.
Do you believe that symbols and what they represent are one and the same thing???
No, we can apply some simple rules to the symbols in certain way to learn things about the object in question.
How does not the fact that many symbols can represent one and the same extant disprove this hypothesis? Is the word "tree" have a brownish trunk and greenish foliage? What about the case where sets of symbols that have more than one possible referent? Consider the word FORD. Does it have wheels and a motor? What is the height of the water that one displaces when we might walk across it? There is a categorical difference between an object and its representations and the fact that one subobject of those categories exists is not proof that a subobject in another category has a given truth value. BTW, truth values are not confined to {True, False}.
For well-defined propositions regarding the numbers I think the values are confined to true or false.
Jason
Jason Resch
On 26 Sep 2011, at 04:42, Pierz wrote:
- it's not well explained in the paper
yet contains the all the really sweeping and startling assertions.
When I presented UDA at the ASSC meeting of 1995 (I think) a "famous" philosopher of mind left the room at step 3 (the duplication step). He pretended that we feel to be at both places at once after a self-duplication experience. It was the first time someone told me this. I don't know if he was sincere. It looks some people want to believe UDA wrong, and are able to dismiss any step.
Was this Chalmers? You mentioned to me at one point that he believed a duplicated person experiences both perspectives. This is a view I can sympathize with, in the sense that we are part of a universal person who experiences all perspectives. A person who steps into a duplicator does experience both Washington and Moscow, but at either position, does not have the memories of the other, and thus so cannot talk about those experiences. It is similar to a person who is tortured, then given a drug to cause total amnesia. Is it not the same person who experienced being tortured?
Jason
Bruno Marchal
On Mon, Sep 26, 2011 at 11:08 AM, Bruno Marchal <mar...@ulb.ac.be> wrote:When I presented UDA at the ASSC meeting of 1995 (I think) a "famous" philosopher of mind left the room at step 3 (the duplication step). He pretended that we feel to be at both places at once after a self-duplication experience. It was the first time someone told me this. I don't know if he was sincere. It looks some people want to believe UDA wrong, and are able to dismiss any step.
On 26 Sep 2011, at 04:42, Pierz wrote:
- it's not well explained in the paper
yet contains the all the really sweeping and startling assertions.
Was this Chalmers? You mentioned to me at one point that he believed a duplicated person experiences both perspectives.
This is a view I can sympathize with, in the sense that we are part of a universal person who experiences all perspectives.
A person who steps into a duplicator does experience both Washington and Moscow, but at either position, does not have the memories of the other, and thus so cannot talk about those experiences. It is similar to a person who is tortured, then given a drug to cause total amnesia. Is it not the same person who experienced being tortured?
Bruno Marchal
On 26 Sep 2011, at 21:44, meekerdb wrote:
> On 9/26/2011 9:08 AM, Bruno Marchal wrote:
>> Suppose that you are currently in state S (which exist by the comp
>> assumption).
>
> But what does "you" refer to?
Your first person view. Or the owner of your first person view,
restricted to that view, without salvia amnesia, if you want.
> The comp assumption seems ambiguous. Is it the assumption that
> "you" are instantiated by a specific computation?
No. Something like that can be part of the consequence, but this is
clearly not assumed. In fact the UD shows that "you" is instantiated
by an infinity of computations.
> Or is it the assumption that your brain could be replaced, without
> you noticing, by a physically different computer, so long as it
> computed the same function (at some level).
Yes.
> These seem slightly different to me and are only identical if QM is
> false and the world is strictly classical and deterministic. At a
> practical level the brain is certainly mostly classical and so I
> might say 'yes' to the doctor even though my artificial brain will
> have slightly different behavoir because it has different
> counterfactual quantum behavior. But this difference seems to
> present a problem when trying to identify "you" within the inifinite
> bundle of computations instantiating a particular state in the UD
> computations.
Why? If my "original brain" is described by QM (without collapse) it
might be said to self-multiply naturally. But that self-multiplication
will be contagious on the UD in that universe, so this will not change
the relative proportion. On the contrary, the UD itself forces a
multiplication to be lived from inside.
As to identify yourself in the UD*, this is just impossible in any
third person ways. But the indeterminacy is on the first person
experiences, not on their description in the UD. So the statistics are
lived from inside. A computation is winning, if indeed you feel to be
alive through its UD instantiation.
Ambiguities remain, but they are part of the measure problem.
>
> Of course if you replace the whole universe with an emulation,
> instead of just my brain, then my emulated brain in the emulated
> universe can have the same behavior as my natural brain in this
> universe.
Yes, and that is why the reasoning will work in the limiting case
where your "generalized brain" is the entire universe described at
some level. The UD will generate all the digital approximation of that
universe, and at some level of approximation, you will not see the
difference, because we are assuming comp.
>
>> The UD generates an infinity of computations going through that
>> state. All what I say is that your future is determined by all
>> those computations, and your self-referential abilities. If from
>> this you can prove that your future is more random than the one
>> observed, then you are beginning to refute rigorously comp. But the
>> math part shows that this is not easy to do. In fact the random
>> inputs confer stability for the programs which exploits that
>> randomness, and again, this is the case for some formulation (à-la
>> Feynman) of QM.
>
> How is this?
Consider the iterated self-duplication experience, like with the
random movie, where you expect to see (correctly) a random movie. The
movie will seem random because the limiting case is described by a
Gaussian (accepting the p = 1/2 for a single duplication). Other
considerations make such a randomness occurring below you substitution
level, so it might be that the only way to stabilize the computations
above the substitution level comes from some phase randomization,
similar to Feynman explanation of why QM minimize the path action. We
need a notion of negative (amplitude) of probability, extracted from
comp, for such a procedure to work, but this is already provided by
the logic of self-reference when we add the non-cul-de-sac assumption
(Dt) to the provability modality (Bp), with p sigma_1. This can be
made enough precise to make sense of how the quantum can be explained
by the digital viewed from the digital creature themselves. No doubt
that a lot of work remain to be done, but that is exactly what I
wanted to show.
Bruno
Stephen P. King
On Mon, Sep 26, 2011 at 12:14 PM, Stephen P. King <step...@charter.net> wrote:
On 9/26/2011 11:52 AM, Jason Resch wrote:
On Mon, Sep 26, 2011 at 9:44 AM, Stephen P. King <step...@charter.net> wrote:
snip
Jason,
I really would like to understand how it is that the truth valuation of a proposition is not dependent on our knowledge of it can be used to affirm the meaning of the referent of that proposition independent of us?
That sentence was hard to parse! If I understand it correctly, you are asking how a truth, independent of our knowledge, can confer meaning to something without us?
[SPK]
Essentially, yes.[SPK]
Things unknown to anyone can have consequences which are eventually do make a difference to beings which are aware of the difference. A comet colliding with the Earth and hitting a pond of unicellular organisms may have drastically altered the course of evolution on our planet. That such a comet impact ocurred is a fact which is either true or false, despite it being independent of anyone's knowledge of it. Yet it has perceptable results.
The web of causes and effects is an aspect of the material universe. I am taking that concept into consideration.[SPK]
Correspondingly, the existence of some mathematical truth (even if not comprehended by anyone) can have effects for observers, in fact, it might explain both the observers themselves and their experiences.
Slow down! "existence of some mathematical truth"??? Do you mean the truth value of some existing mathematical statement? That is what I mean in my question by the phrase "truth valuation of a proposition". Is a truth value something that exists or does not exist?
I am not sure what you mean by "exists" in this case so let me say this, the state of being true, or the state of being false, for the proposition in question, was settled before a human made a determination regarding that proposition.
[SPK]
Is the "state of being true" a physical state, like the "state of having 10 units of momentum"? Is there a "truth detector"? Are you sure that "state" and "true" are words that go together? AFAIK, true (or false) are values, like numbers. In fact logics can have truth values that range over any set of numbers. This puts truth valuations in the same category as numbers. No?
[SPK]
How does the sentence "17 is prime is a true statement" confer implicit meaning to its referent?
What is the referent in this case? 17? And what do you mean by "meaning"? 17's primality is a fact of nature. The statement's existence or non-existence, comprehension or non-comprehension makes no difference to 17, only what you could say we humans have discovered about 17.
Is the symbol 17 the same extant as the abstract number it refers to?
No, as I mentioned to Brent in a post the other day, we ought not confuse the label for the thing. Nor should we confuse our idea of a thing for the thing itself.
OK, does not this imply that there are (at least) two separate categories: Labels and Things? What relation might exist between these categories?
Do you believe that symbols and what they represent are one and the same thing???
No, we can apply some simple rules to the symbols in certain way to learn things about the object in question.
What relation might exist between the "rules" of symbols and the "rules" of things?
How does not the fact that many symbols can represent one and the same extant disprove this hypothesis? Is the word "tree" have a brownish trunk and greenish foliage? What about the case where sets of symbols that have more than one possible referent? Consider the word FORD. Does it have wheels and a motor? What is the height of the water that one displaces when we might walk across it? There is a categorical difference between an object and its representations and the fact that one subobject of those categories exists is not proof that a subobject in another category has a given truth value. BTW, truth values are not confined to {True, False}.
For well-defined propositions regarding the numbers I think the values are confined to true or false.
Jason
--[SPK]
Not in general, unless one is only going to allow only Boolean logics to exist. There have been proven to exist logics that have truth values that range over any set of numbers, not just {0,1}. Recall the requirement for a mathematical structure to exist: Self-consistency.
Onward!
Stephen
Jason Resch
On 9/26/2011 7:56 PM, Jason Resch wrote:
On Mon, Sep 26, 2011 at 12:14 PM, Stephen P. King <step...@charter.net> wrote:
[SPK]On 9/26/2011 11:52 AM, Jason Resch wrote:
On Mon, Sep 26, 2011 at 9:44 AM, Stephen P. King <step...@charter.net> wrote:
Jason,snip
I really would like to understand how it is that the truth valuation of a proposition is not dependent on our knowledge of it can be used to affirm the meaning of the referent of that proposition independent of us?
That sentence was hard to parse! If I understand it correctly, you are asking how a truth, independent of our knowledge, can confer meaning to something without us?
Essentially, yes.[SPK]
Things unknown to anyone can have consequences which are eventually do make a difference to beings which are aware of the difference. A comet colliding with the Earth and hitting a pond of unicellular organisms may have drastically altered the course of evolution on our planet. That such a comet impact ocurred is a fact which is either true or false, despite it being independent of anyone's knowledge of it. Yet it has perceptable results.
The web of causes and effects is an aspect of the material universe. I am taking that concept into consideration.[SPK]
Correspondingly, the existence of some mathematical truth (even if not comprehended by anyone) can have effects for observers, in fact, it might explain both the observers themselves and their experiences.
Slow down! "existence of some mathematical truth"??? Do you mean the truth value of some existing mathematical statement? That is what I mean in my question by the phrase "truth valuation of a proposition". Is a truth value something that exists or does not exist?
I am not sure what you mean by "exists" in this case so let me say this, the state of being true, or the state of being false, for the proposition in question, was settled before a human made a determination regarding that proposition.
[SPK]
Is the "state of being true" a physical state, like the "state of having 10 units of momentum"?
If the object under consideration is a physical object, you might be able to say that. If the object under consideration is 17, I would say no.
Is there a "truth detector"?
There can be truth detectors, in some sense we may be truth detectors, but us discovery of a truth is not what makes it true.
Are you sure that "state" and "true" are words that go together?
I am at a loss for an english word that conveys the status of true or false. We have the word parity for the status of even or odd, for example, but I could not think of such a word that conveys the same for true or false, which is why I used "the state of being true or false".
AFAIK, true (or false) are values, like numbers. In fact logics can have truth values that range over any set of numbers. This puts truth valuations in the same category as numbers. No?
True and false can be represented by two different numbers, but I am not sure that makes them values in the same sense of numbers.
[SPK][SPK]
How does the sentence "17 is prime is a true statement" confer implicit meaning to its referent?
What is the referent in this case? 17? And what do you mean by "meaning"? 17's primality is a fact of nature. The statement's existence or non-existence, comprehension or non-comprehension makes no difference to 17, only what you could say we humans have discovered about 17.
Is the symbol 17 the same extant as the abstract number it refers to?
No, as I mentioned to Brent in a post the other day, we ought not confuse the label for the thing. Nor should we confuse our idea of a thing for the thing itself.
OK, does not this imply that there are (at least) two separate categories: Labels and Things? What relation might exist between these categories?
Labels are a human invention to support communication of ideas, which you might say is yet another category of things.
The relation ship might be as follows: if I tell you to multiply 1200 x 1800, you could arrange 1800 rows of 1200 beans and count them all, or you could follow some simple rules of transformation applied to the labels '1200' and '1800' and have a shortcut to the answer, without having to do all that counting.
[SPK]Do you believe that symbols and what they represent are one and the same thing???
No, we can apply some simple rules to the symbols in certain way to learn things about the object in question.
What relation might exist between the "rules" of symbols and the "rules" of things?
I think I covered this above.
[SPK]How does not the fact that many symbols can represent one and the same extant disprove this hypothesis? Is the word "tree" have a brownish trunk and greenish foliage? What about the case where sets of symbols that have more than one possible referent? Consider the word FORD. Does it have wheels and a motor? What is the height of the water that one displaces when we might walk across it? There is a categorical difference between an object and its representations and the fact that one subobject of those categories exists is not proof that a subobject in another category has a given truth value. BTW, truth values are not confined to {True, False}.
For well-defined propositions regarding the numbers I think the values are confined to true or false.
Jason
--
Not in general, unless one is only going to allow only Boolean logics to exist. There have been proven to exist logics that have truth values that range over any set of numbers, not just {0,1}. Recall the requirement for a mathematical structure to exist: Self-consistency.
Okay, there may be other subjects, besides number theory and arithmetical truth where other forms of logic are more appropriate. For unambiguous propositions about numbers, do you agree with the law of the excluded middle?
Jason
Stephen P. King
On Tue, Sep 27, 2011 at 6:49 AM, Stephen P. King <step...@charter.net> wrote:
On 9/26/2011 7:56 PM, Jason Resch wrote:
On Mon, Sep 26, 2011 at 12:14 PM, Stephen P. King <step...@charter.net> wrote:
[SPK]On 9/26/2011 11:52 AM, Jason Resch wrote:
On Mon, Sep 26, 2011 at 9:44 AM, Stephen P. King <step...@charter.net> wrote:
Jason,snip
I really would like to understand how it is that the truth valuation of a proposition is not dependent on our knowledge of it can be used to affirm the meaning of the referent of that proposition independent of us?
That sentence was hard to parse! If I understand it correctly, you are asking how a truth, independent of our knowledge, can confer meaning to something without us?
Essentially, yes.[SPK]
Things unknown to anyone can have consequences which are eventually do make a difference to beings which are aware of the difference. A comet colliding with the Earth and hitting a pond of unicellular organisms may have drastically altered the course of evolution on our planet. That such a comet impact ocurred is a fact which is either true or false, despite it being independent of anyone's knowledge of it. Yet it has perceptable results.
The web of causes and effects is an aspect of the material universe. I am taking that concept into consideration.[SPK]
Correspondingly, the existence of some mathematical truth (even if not comprehended by anyone) can have effects for observers, in fact, it might explain both the observers themselves and their experiences.
Slow down! "existence of some mathematical truth"??? Do you mean the truth value of some existing mathematical statement? That is what I mean in my question by the phrase "truth valuation of a proposition". Is a truth value something that exists or does not exist?
I am not sure what you mean by "exists" in this case so let me say this, the state of being true, or the state of being false, for the proposition in question, was settled before a human made a determination regarding that proposition.
[SPK]
Is the "state of being true" a physical state, like the "state of having 10 units of momentum"?
If the object under consideration is a physical object, you might be able to say that. If the object under consideration is 17, I would say no.
OK. So it is your belief that , in general, objects (of any categorical type) have specific and definite properties absent the specification of the means of observation? How do you explain the existence of conjugate observables in QM?
Is there a "truth detector"?
There can be truth detectors, in some sense we may be truth detectors, but us discovery of a truth is not what makes it true.
Are you sure that "state" and "true" are words that go together?
I am at a loss for an english word that conveys the status of true or false. We have the word parity for the status of even or odd, for example, but I could not think of such a word that conveys the same for true or false, which is why I used "the state of being true or false".
AFAIK, true (or false) are values, like numbers. In fact logics can have truth values that range over any set of numbers. This puts truth valuations in the same category as numbers. No?
True and false can be represented by two different numbers, but I am not sure that makes them values in the same sense of numbers.
I was mentioning the fact that logics with truth values that range over different sets of values have been proven to exist. Logic is not limited to truth values over {0,1}, only Boolean logics are so restricted by their defining rules.
[SPK][SPK]
How does the sentence "17 is prime is a true statement" confer implicit meaning to its referent?
What is the referent in this case? 17? And what do you mean by "meaning"? 17's primality is a fact of nature. The statement's existence or non-existence, comprehension or non-comprehension makes no difference to 17, only what you could say we humans have discovered about 17.
Is the symbol 17 the same extant as the abstract number it refers to?
No, as I mentioned to Brent in a post the other day, we ought not confuse the label for the thing. Nor should we confuse our idea of a thing for the thing itself.
OK, does not this imply that there are (at least) two separate categories: Labels and Things? What relation might exist between these categories?
Labels are a human invention to support communication of ideas, which you might say is yet another category of things.
Interesting. We "invented" labels. So representations, in general, are they inventions also?
The relation ship might be as follows: if I tell you to multiply 1200 x 1800, you could arrange 1800 rows of 1200 beans and count them all, or you could follow some simple rules of transformation applied to the labels '1200' and '1800' and have a shortcut to the answer, without having to do all that counting.
Is counting a uniquely human activity? Could not the behavior of any physical system that has some dynamic behavior (f. ex. not restricted to a single point in its configuration/state/phase space) be considered as a form of counting? Is measurement in general not a form of counting?
[SPK]Do you believe that symbols and what they represent are one and the same thing???
No, we can apply some simple rules to the symbols in certain way to learn things about the object in question.
What relation might exist between the "rules" of symbols and the "rules" of things?
I think I covered this above.
Is this relation an invention or a fact that was discovered? Could you elaborate on your thoughts of this relation. Does it have a general form?
[SPK]How does not the fact that many symbols can represent one and the same extant disprove this hypothesis? Is the word "tree" have a brownish trunk and greenish foliage? What about the case where sets of symbols that have more than one possible referent? Consider the word FORD. Does it have wheels and a motor? What is the height of the water that one displaces when we might walk across it? There is a categorical difference between an object and its representations and the fact that one subobject of those categories exists is not proof that a subobject in another category has a given truth value. BTW, truth values are not confined to {True, False}.
For well-defined propositions regarding the numbers I think the values are confined to true or false.
Jason
--
Not in general, unless one is only going to allow only Boolean logics to exist. There have been proven to exist logics that have truth values that range over any set of numbers, not just {0,1}. Recall the requirement for a mathematical structure to exist: Self-consistency.
Okay, there may be other subjects, besides number theory and arithmetical truth where other forms of logic are more appropriate. For unambiguous propositions about numbers, do you agree with the law of the excluded middle?
For logics that have a form of excluded middle law, yes. But those are not the only form of logic. Heyting logics, for example, are different. Is it necessarily the case that a logic must contain the law of excluded middle to be "unambiguous"? If the rules and axioms are well formed and self-consistent, why is the LEM necessary? For example, there are logics that have truth values over {-1, 0,1}. Are they necessarily ambiguous because of this?
Onward!
Stephen
Bruno Marchal
On 27 Sep 2011, at 13:49, Stephen P. King wrote:
> On 9/26/2011 7:56 PM, Jason Resch wrote:
<snip>
>> For well-defined propositions regarding the numbers I think the
>> values are confined to true or false.
>>
>> Jason
>>
>> --
> [SPK]
> Not in general, unless one is only going to allow only Boolean
> logics to exist. There have been proven to exist logics that have
> truth values that range over any set of numbers, not just {0,1}.
> Recall the requirement for a mathematical structure to exist: Self-
> consistency.
Consistency is a notion applied usually to theories, or (chatty)
machines, not to mathematical structures.
A theory is consistent if it does not prove some proposition and its
negation. A machine is consistent if it does not assert a proposition
and its negation.
In first order logic we have Gödel-Henkin completeness theorem which
shows that a theory is consistent if and only if there is a
mathematical structure (called model) satisfying (in a sense which can
be made precise) the proposition proved in the theory.
Also, it is true that classical (Boolean) logic are not the only
logic. There are infinitely many logics, below and above classical
propositional logic. But this cannot be used to criticize the use of
classical logic in some domain.
All treatises on any non classical logic used classical (or much more
rarely intuitionistic) logic at the meta-level. You will not find a
book on fuzzy logic having fuzzy theorems, for example. Non classical
logics have multiple use, which are not related with the kind of ontic
truth we are looking for when searching a TOE.
Usually non classical logic have epistemic or pragmatic classical
interpretations, or even classical formulation, like the classical
modal logic S4 which can emulate intuitionistic logic, or the
Brouwersche modal logic B, which can emulate weak quantum logic. This
corresponds to the fact that intuitionist logic might modelize
constructive provability, and quantum logic modelizes observability,
and not the usual notion of classical truth (as used almost everywhere
in mathematics).
To invoke the existence of non classical logic to throw a doubt about
the universal truth of elementary statements in well defined domain,
like arithmetic, would lead to complete relativism, given that you can
always build some ad hoc logic/theory proving the negation of any
statement, and this would make the notion of truth problematic. The
contrary is true. A non classical logic is eventually accepted when we
can find an interpretation of it in the classical framework.
A non standard truth set, like the collection of open subsets of a
topological space, provided a classical sense for intuitionist logic,
like a lattice of linear subspaces can provide a classical
interpretation of quantum logic (indeed quantum logic is born from
such structures). It might be that nature observables obeys quantum
logic, but quantum physicists talk and reason in classical logic, and
use classical mathematical tools to describe the non classical
behavior of matter.
Bruno
meekerdb
> [SPK]
> Not in general, unless one is only going to allow only Boolean logics to exist.
> There have been proven to exist logics that have truth values that range over any set of
> numbers, not just {0,1}. Recall the requirement for a mathematical structure to exist:
> Self-consistency.
>
> Onward!
>
> Stephen
How do you define consistency for fuzzy or probabilistic logics? If you prove P(x)=0.1
and P(x)=0.2 is that inconsistency?
Brent
meekerdb
Brent
Jason Resch
I think this an assumption or another axiom. Consider the conjecture that every even number can be written as the sum of two primes. Suppose there is no proof of this from Peano's axioms, but we can't know that there is no proof; only that we can't find one. Intuitively we think the conjecture must be true or false, but this is based on the idea that if we tested all the evens we'd find it either true or false of each one. Yet infinite testing is impossible. So if the conjecture is true but unprovable, then it's undecidable.Not in general, unless one is only going to allow only Boolean logics to exist. There have been proven to exist logics that have truth values that range over any set of numbers, not just {0,1}. Recall the requirement for a mathematical structure to exist: Self-consistency.
Okay, there may be other subjects, besides number theory and arithmetical truth where other forms of logic are more appropriate. For unambiguous propositions about numbers, do you agree with the law of the excluded middle?
Jason
In any case, whether or not some proposition is decidable (can be demonstrated as true or demonstrated as false in a series of logical steps leading to the axioms in question) does not suggest that a mathematical proposition is true or false dependently of us. Conversely, I think it is one of the strongest arguments against the idea that math is man-made. Any system of axioms we develop is imperfect in the sense that it cannot answer all questions concerning the numbers.
Those who think that the objects of study in mathematics are human inventions are living in the early 20th century.
Jason
Jason Resch
Yes I believe objects have properties even if unobserved. Do you really believe the cat is both alive and dead (in the same universe) until it is observed?
How do you explain the existence of conjugate observables in QM?
If you are a CI proponent, you could say being in many places at once, or having many simultaneous states simultaneously is a property of objects in superposition. The Everettian might say a more simply that a property of a particle (or the universe) is that it obeys the Shrodinger equation.
I assume your point is that an particle cannot have a definite momentum and position, but this is really a statement about observation (the observer cannot know both simultaneously), not the object (or many objects) under consideration.
[SPK]
Is there a "truth detector"?
There can be truth detectors, in some sense we may be truth detectors, but us discovery of a truth is not what makes it true.
Are you sure that "state" and "true" are words that go together?
I am at a loss for an english word that conveys the status of true or false. We have the word parity for the status of even or odd, for example, but I could not think of such a word that conveys the same for true or false, which is why I used "the state of being true or false".
AFAIK, true (or false) are values, like numbers. In fact logics can have truth values that range over any set of numbers. This puts truth valuations in the same category as numbers. No?
True and false can be represented by two different numbers, but I am not sure that makes them values in the same sense of numbers.
I was mentioning the fact that logics with truth values that range over different sets of values have been proven to exist. Logic is not limited to truth values over {0,1}, only Boolean logics are so restricted by their defining rules.
I think Bruno addressed this very well.
[SPK]
[SPK][SPK]
How does the sentence "17 is prime is a true statement" confer implicit meaning to its referent?
What is the referent in this case? 17? And what do you mean by "meaning"? 17's primality is a fact of nature. The statement's existence or non-existence, comprehension or non-comprehension makes no difference to 17, only what you could say we humans have discovered about 17.
Is the symbol 17 the same extant as the abstract number it refers to?
No, as I mentioned to Brent in a post the other day, we ought not confuse the label for the thing. Nor should we confuse our idea of a thing for the thing itself.
OK, does not this imply that there are (at least) two separate categories: Labels and Things? What relation might exist between these categories?
Labels are a human invention to support communication of ideas, which you might say is yet another category of things.
Interesting. We "invented" labels. So representations, in general, are they inventions also?
Some representations are human inventions.
[SPK]
The relation ship might be as follows: if I tell you to multiply 1200 x 1800, you could arrange 1800 rows of 1200 beans and count them all, or you could follow some simple rules of transformation applied to the labels '1200' and '1800' and have a shortcut to the answer, without having to do all that counting.
Is counting a uniquely human activity?
No, Elephants, and even fish have been shown to count.
Could not the behavior of any physical system that has some dynamic behavior (f. ex. not restricted to a single point in its configuration/state/phase space) be considered as a form of counting?
I would say it is a form of progression, counting has too different a connotation I think.
Is measurement in general not a form of counting?
I think it depends on what is being measured. I'm not sure where you are going with this.
[SPK]
[SPK]Do you believe that symbols and what they represent are one and the same thing???
No, we can apply some simple rules to the symbols in certain way to learn things about the object in question.
What relation might exist between the "rules" of symbols and the "rules" of things?
I think I covered this above.
Is this relation an invention or a fact that was discovered?
Our system of decimal representation is in some sense an invention, but the fact that theorem building can be framed in terms of string/symbol manipulations is the fact on which that invention is based. The analogy is the Apollo rocket was an invention, but it depends on the foundation of physics discovered by Newton.
Could you elaborate on your thoughts of this relation. Does it have a general form?
Which relation?
[SPK]
[SPK]How does not the fact that many symbols can represent one and the same extant disprove this hypothesis? Is the word "tree" have a brownish trunk and greenish foliage? What about the case where sets of symbols that have more than one possible referent? Consider the word FORD. Does it have wheels and a motor? What is the height of the water that one displaces when we might walk across it? There is a categorical difference between an object and its representations and the fact that one subobject of those categories exists is not proof that a subobject in another category has a given truth value. BTW, truth values are not confined to {True, False}.
For well-defined propositions regarding the numbers I think the values are confined to true or false.
Jason
--
Not in general, unless one is only going to allow only Boolean logics to exist. There have been proven to exist logics that have truth values that range over any set of numbers, not just {0,1}. Recall the requirement for a mathematical structure to exist: Self-consistency.
Okay, there may be other subjects, besides number theory and arithmetical truth where other forms of logic are more appropriate. For unambiguous propositions about numbers, do you agree with the law of the excluded middle?
For logics that have a form of excluded middle law, yes.
So you believe every unambiguous proposition regarding the numbers is either true or false. Even the ones we have not yet proved, like Goldbach's conjecture. If so we don't need to observe a proof or disproof of Goldbach's conjecture for it to be true or false.
But those are not the only form of logic. Heyting logics, for example, are different. Is it necessarily the case that a logic must contain the law of excluded middle to be "unambiguous"? If the rules and axioms are well formed and self-consistent, why is the LEM necessary? For example, there are logics that have truth values over {-1, 0,1}. Are they necessarily ambiguous because of this?
I don't know enough about these logics to say.
Jason
meekerdb
>
> On 26 Sep 2011, at 21:44, meekerdb wrote:
>
>> On 9/26/2011 9:08 AM, Bruno Marchal wrote:
>>> Suppose that you are currently in state S (which exist by the comp assumption).
>>
>> But what does "you" refer to?
>
> Your first person view. Or the owner of your first person view, restricted to that view,
> without salvia amnesia, if you want.
>
>
>> The comp assumption seems ambiguous. Is it the assumption that "you" are instantiated
>> by a specific computation?
>
> No. Something like that can be part of the consequence, but this is clearly not assumed.
> In fact the UD shows that "you" is instantiated by an infinity of computations.
>
>
>
>> Or is it the assumption that your brain could be replaced, without you noticing, by a
>> physically different computer, so long as it computed the same function (at some level).
>
> Yes.
>
>
>> These seem slightly different to me and are only identical if QM is false and the world
>> is strictly classical and deterministic. At a practical level the brain is certainly
>> mostly classical and so I might say 'yes' to the doctor even though my artificial brain
>> will have slightly different behavoir because it has different counterfactual quantum
>> behavior. But this difference seems to present a problem when trying to identify "you"
>> within the inifinite bundle of computations instantiating a particular state in the UD
>> computations.
>
> Why? If my "original brain" is described by QM (without collapse) it might be said to
> self-multiply naturally. But that self-multiplication will be contagious on the UD in
> that universe, so this will not change the relative proportion.
That's the step that seems ambiguous. What you write above applies to a physically
realized (i.e. quantum) UD, but not to the UD in Platonia. The physically realized UD
will have non-zero probabilities of doing something random instead of implementing the
intended function.
> On the contrary, the UD itself forces a multiplication to be lived from inside.
> As to identify yourself in the UD*, this is just impossible in any third person ways.
> But the indeterminacy is on the first person experiences, not on their description in
> the UD. So the statistics are lived from inside. A computation is winning, if indeed you
> feel to be alive through its UD instantiation.
> Ambiguities remain, but they are part of the measure problem.
>
>
>
>>
>> Of course if you replace the whole universe with an emulation, instead of just my
>> brain, then my emulated brain in the emulated universe can have the same behavior as my
>> natural brain in this universe.
>
> Yes, and that is why the reasoning will work in the limiting case where your
> "generalized brain" is the entire universe described at some level. The UD will generate
> all the digital approximation of that universe, and at some level of approximation, you
> will not see the difference, because we are assuming comp.
>
>
>
>>
>>> The UD generates an infinity of computations going through that state. All what I say
>>> is that your future is determined by all those computations, and your self-referential
>>> abilities. If from this you can prove that your future is more random than the one
>>> observed, then you are beginning to refute rigorously comp. But the math part shows
>>> that this is not easy to do. In fact the random inputs confer stability for the
>>> programs which exploits that randomness, and again, this is the case for some
>>> formulation (�-la Feynman) of QM.
>>
>> How is this?
>
> Consider the iterated self-duplication experience, like with the random movie, where you
> expect to see (correctly) a random movie. The movie will seem random because the
> limiting case is described by a Gaussian (accepting the p = 1/2 for a single
> duplication). Other considerations make such a randomness occurring below you
> substitution level, so it might be that the only way to stabilize the computations above
> the substitution level comes from some phase randomization, similar to Feynman
> explanation of why QM minimize the path action.
So you're talking about keeping the computation classical, even though realized by a
physical device which is microscopically quantum? I don't recognize the reference to "the
random movie".
> We need a notion of negative (amplitude) of probability,
Negative probability or negative, imaginary probability amplitude?
> extracted from comp, for such a procedure to work, but this is already provided by the
> logic of self-reference when we add the non-cul-de-sac assumption (Dt) to the
> provability modality (Bp), with p sigma_1. This can be made enough precise to make sense
> of how the quantum can be explained by the digital viewed from the digital creature
> themselves. No doubt that a lot of work remain to be done, but that is exactly what I
> wanted to show.
You lost me.
Brent
Stephen P. King
thorough explanation of fuzzy logic in any of Bart Kosko's books on the
subject. I am sure that there are papers and or books that explain the
same for probabilistic logic.
Onward!
Pierz
brought me a lot closer to grasping the essence of this argument. I
can see that the set of integers is also the set of all possible
information states, and that the difference between that and the UD is
the element of sequential computation. I can also see that my
objection to infinite computational resources and state memory comes
from the 1-p perspective. For me, in the "physical" universe, any
computation is restricted by the laws of matter and must be embedded
in that matter. Now one of the fascinating revelations of the
computational approach to physics is the fact that a quantity such as
position can only be defined to a certain level of precision by the
universe itself because the universe has finite informational
resources at its disposal. This was my objection to the UD. But I can
see that this restriction need not necessarily apply at the 'higher' 3-
p level of the UD's computations. What interests me is the question:
does UDA predict that the 1-p observer will see a universe with such
restrictions? If it explains why the 1-p observer seems to exist in a
world where there is only a finite number of bits available, despite
existing in a machine with an infinite level of bit resolution, then
that would be a most interesting result. Otherwise, it seems to me to
remain a problem for the theory, or at least a question in need of an
answer, like dark matter in cosmology.
I am going to have to meditate further on arithmetical realism. I
don't believe in objective matter either (it seems refuted by Bell's
Theorem anyway), but a chasm seems to lie between the statement "17
is prime" and "the UDA (Robinson arithmetic) executes all possible
programs". The problem is one of instantiation. I can conceive of a
universe - a singularity perhaps, with only one bit of information -
in which the statement "17 is prime" can never be made. To formulate,
ie instantiate, 17, requires a certain amount of information. To say
that a program executes, as opposed to saying it merely is implied by
a set of theoretical axioms, requires the instantiation of that
algorithm. I suppose this is a restatement of the problem above.
Arithemetical realism then would be the postulate that everything
implied in arithmetic is actually instantiated. It seems to me I can
grant 17 is prime, without granting this instantiation of everything.
I'm also troubled by the statement that you have proved in the AUDA
that any Lobian machine can apprehend the UDA. Is not a three-year-old
child and a cat a Lobian machine? Or indeed my senile father. How can
you assert they could comprehend such an abstraction? Either they
aren't Lobian machines, or there's hole in the proof somewhere,
surely!
Jason mentions the anthropic principle (which of course I'm well
acquainted with) and the idea of the computations which contain
observers. I have read, without following, some of your propositions
involving the Beweisbar predicate and self-referential relations and
what have you. Is that the formalism that is supposed to define which
computations are conscious? Is there a summary somewhere? I am
wondering how consciousness can possibly be an attribute of some
computations and not others, and why, if it's a matter of some certain
mathematical properties of the computations, we could not fairly
easily write a conscious algorithm? Surely complexity can't be the
defining feature (at what arbitrary level of complexity does the light
come on?), so it should be a simple matter. (Though the proof of
having created consciousness in the program would be a problem!) Don't
we have to define consciousness (not necessarily self-awareness, or
the awareness of being aware) as a property of numbers per se?
Sadly when you start to talk about the difficulty of proving that our
histories in the UD are more random than the actual histories we
observe, I can't follow you any more - too much theory I'm unfamiliar
with. I can see however that many (nearly all) of the infinite
computations passing through our aware states will destroy us, as it
were, so we can never exist in those computations (sort of anthropic
principle). This also suggests a kind of immortality, the same kind as
I propose in a blog post I wrote called the 'cryogenic paradox' in
which I argue that there can only be a single observer, a single locus
of consciousness underlying all apparently separate consciousnesses,
which would really be just different perspectives of this one
observer. It seems irresistible as a conclusion (from philosophical
arguments quite different to the UDA), and yet also kind of horrific.
Only a sort of state-bound recall barrier prevents us from being aware
that we suffer every fate possible.
I agree re academia. From all I can observe, it is a viper's pit. The
ground of accepted truth is fought over as hard as any piece of the
Holy Land, and in this as in all struggles, power matters. It is
hardly the free and unbiased exchange between equal and curious minds!
We are not so different today from the cardinals who refused to look
down Galileo's telescope.
Finally, I despise all theory that makes obscurity a virtue. Compare
Lacan's tedious impenetrability with Einstein's almost childish
simplicity and profundity. Obscurity is the darkness which merely
clever minds use to cover their nakedness (to invoke the emperor
again). No insult to you, Bruno, intended, this time.
Jason Resch
OK, well I think this and the other responses (notably Jason's) have
brought me a lot closer to grasping the essence of this argument. I
can see that the set of integers is also the set of all possible
information states, and that the difference between that and the UD is
the element of sequential computation. I can also see that my
objection to infinite computational resources and state memory comes
from the 1-p perspective. For me, in the "physical" universe, any
computation is restricted by the laws of matter and must be embedded
in that matter. Now one of the fascinating revelations of the
computational approach to physics is the fact that a quantity such as
position can only be defined to a certain level of precision by the
universe itself because the universe has finite informational
resources at its disposal. This was my objection to the UD. But I can
see that this restriction need not necessarily apply at the 'higher' 3-
p level of the UD's computations. What interests me is the question:
does UDA predict that the 1-p observer will see a universe with such
restrictions? If it explains why the 1-p observer seems to exist in a
world where there is only a finite number of bits available, despite
existing in a machine with an infinite level of bit resolution, then
that would be a most interesting result. Otherwise, it seems to me to
remain a problem for the theory, or at least a question in need of an
answer, like dark matter in cosmology.
I am going to have to meditate further on arithmetical realism.
I
don't believe in objective matter either (it seems refuted by Bell's
Theorem anyway),
but a chasm seems to lie between the statement "17
is prime" and "the UDA (Robinson arithmetic) executes all possible
programs". The problem is one of instantiation. I can conceive of a
universe - a singularity perhaps, with only one bit of information -
in which the statement "17 is prime" can never be made. To formulate,
ie instantiate, 17, requires a certain amount of information.
To say
that a program executes, as opposed to saying it merely is implied by
a set of theoretical axioms, requires the instantiation of that
algorithm. I suppose this is a restatement of the problem above.
Arithemetical realism then would be the postulate that everything
implied in arithmetic is actually instantiated. It seems to me I can
grant 17 is prime, without granting this instantiation of everything.
Sadly when you start to talk about the difficulty of proving that our
histories in the UD are more random than the actual histories we
observe, I can't follow you any more - too much theory I'm unfamiliar
with. I can see however that many (nearly all) of the infinite
computations passing through our aware states will destroy us, as it
were, so we can never exist in those computations (sort of anthropic
principle). This also suggests a kind of immortality, the same kind as
I propose in a blog post I wrote called the 'cryogenic paradox' in
which I argue that there can only be a single observer, a single locus
of consciousness underlying all apparently separate consciousnesses,
which would really be just different perspectives of this one
observer. It seems irresistible as a conclusion (from philosophical
arguments quite different to the UDA), and yet also kind of horrific.
Only a sort of state-bound recall barrier prevents us from being aware
that we suffer every fate possible.
Bruno Marchal
Pierz
existence of
> some would imply the existence of all.
I agree that all mathematical constructs must have the same kind of
existence, the same ontological status. But I see a distinction
between the type of existence pi has, and the type of existence that
time, space and matter have. Well, obviously. The question is, are
they prior to such instantiated entities, or emergent from them?
Similar to the question, are physical laws objectively extant, or mere
descriptions of 'habits'?
> Do you agree that at least something has to be primitively real?
prior reality, a spiritual position I suppose, though I also believe
these categories may well just be prejudices in our mental make-up.
For physicists, it's the quantum field, for mathematicians it's
number, for saints it is love. All perhaps faces of an unnameable
prior something. I've read Bruno arguing for number's capacity to
explain qualia, and I find it unconvincing. Mathematics is pure
structure and qualia are non structural, non quantifiable, not that
they are 'uncomputable', but just don't fall into the computable/
uncomputable opposition at all. If a person had no right brain at all,
he might argue the way Bruno does on this point. (I'm worried about
insulting him again now. I don't mean it's half brained. I mean it is
blind to all but the quantifiable, and therefore will never satisfy an
artist, for instance). So qualia make me prefer to seek my ontological
roots in the notion of consciousness rather than number.
> We also are aware of every possible goodness or blessing. At a minimum,
> this realization should compel us to treat each other better. In the end,
> the conclusion is little different from the golden rule or the concept of
> karma. All the good things we do are experienced by others (ourselves),
> same with all the bad things.
I mentioned on the subject. If we knew this, truly believed in this
unity of the observer, we would move quick smart to a society
optimized for the benefit of all. We can never gain at another's
expense. Not "There but for the grace of God go I" but simply "There
go I."
On Sep 28, 3:09 pm, Jason Resch <jasonre...@gmail.com> wrote:
Bruno Marchal
Why. In platonia the UD is multiplied, in all possible ways, including
the quantum one.
> The physically realized UD will have non-zero probabilities of doing
> something random instead of implementing the intended function.
And? What would that change anything in the reasoning?
And what do you mean by physically realized?
>>>> (à-la Feynman) of QM.
>>>
>>> How is this?
>>
>> Consider the iterated self-duplication experience, like with the
>> random movie, where you expect to see (correctly) a random movie.
>> The movie will seem random because the limiting case is described
>> by a Gaussian (accepting the p = 1/2 for a single duplication).
>> Other considerations make such a randomness occurring below you
>> substitution level, so it might be that the only way to stabilize
>> the computations above the substitution level comes from some phase
>> randomization, similar to Feynman explanation of why QM minimize
>> the path action.
>
> So you're talking about keeping the computation classical, even
> though realized by a physical device which is microscopically quantum?
Computation is a classical notion at the start. Also, the UD Argument
does not assume quantum mechanics, nor any physical theories. It
assumes only that a physical reality exist do that the notion of
doctor, hospital, brain, and enough concrete computer can exist, so
that it makes sense to say "yes" to a digitalist doctor.
At the start of the reasoning it is better to be agnostic on
physicalism.
> I don't recognize the reference to "the random movie".
It is the thought experience where you are multiplied in 2^(16180 *
10000) versions, each in front of a different image on a black and
white screen having 16180 * 10000 pixels. And this 24 times per
second, during 90 minutes.
The question is: what is more probable among the following: you will
feel to be
- in front of a black screen for one hour and half
- in front of a white screen for one hour and half
- in front of a screen with the movie "Shadow of a Doubt "by Hitchcock
- in front of white noise snow, but actually it gives the first (16180
* 10000) * (60 * 90) * 24 decimal of Pi.
- in front of white noise
- - in front of a screen with the movie "Shadow of a Doubt "by
Hitchcock with chinese subtitle.
Now, note that the UD, by its excessive dumbness, multiplies each
computation, in that way, by dovetailing it on the real as dummy
argument, so that our comp global (in front of a UD) indeterminacy has
to take this into account.
>
>> We need a notion of negative (amplitude) of probability,
>
> Negative probability or negative, imaginary probability amplitude?
We have good evidence for the last (imaginary probability amplitude),
but only the future will decide. Well, technically the Z and X
material hypostases are going in the same direction.
>
>> extracted from comp, for such a procedure to work, but this is
>> already provided by the logic of self-reference when we add the non-
>> cul-de-sac assumption (Dt) to the provability modality (Bp), with p
>> sigma_1. This can be made enough precise to make sense of how the
>> quantum can be explained by the digital viewed from the digital
>> creature themselves. No doubt that a lot of work remain to be done,
>> but that is exactly what I wanted to show.
>
> You lost me.
Let me put it in this way. I interview classical platonist machines,
being ideally correct (they never emit arithmetically unsound
statements). Bp = the machine rationally believes p (and this means
that the machine believes this instinctively (p is some axiom), or can
derive it from such axioms by using the usual inference rules.
Knowledge is given by Bp & p (following Theaetetus).
Observation is given by Bp & Dt (so that we get the "probability"
notion in the way made obligatory by the UD Argument). Dt is the non
cul-de-sac assumption, so that "probability" has a meaning.
Physical observation is the same as observation, except that p has to
be restricted to the sigma_1 sentences, so as to restrict the
probabilities on the UD computations. This gives the Z1 and Z1* logic.
The logic of quanta observable appears in Z1*. The qualia appears in
X1* (the same but with the modal variant given by Bp & Dt & p; we just
reapply the Theaetetus idea).
Bruno
Stephen P. King
On 27 Sep 2011, at 13:49, Stephen P. King wrote:
On 9/26/2011 7:56 PM, Jason Resch wrote:
<snip>
For well-defined propositions regarding the numbers I think the values are confined to true or false.[SPK]
Jason
--
Not in general, unless one is only going to allow only Boolean logics to exist. There have been proven to exist logics that have truth values that range over any set of numbers, not just {0,1}. Recall the requirement for a mathematical structure to exist: Self-consistency.
Consistency is a notion applied usually to theories, or (chatty) machines, not to mathematical structures.
A theory is consistent if it does not prove some proposition and its negation. A machine is consistent if it does not assert a proposition and its negation.
Is not a machine represented mathematically by some abstract (mathematical ) structure? I am attempting to find clarity in the ideas surrounding the notion of "machine" and how you arrive at the idea that the abstract notion of implementation is sufficient to derive the physical notion of implementation.
In first order logic we have Gödel-Henkin completeness theorem which shows that a theory is consistent if and only if there is a mathematical structure (called model) satisfying (in a sense which can be made precise) the proposition proved in the theory.
What constraints are defined on the models by the Gödel-Henkin completeness theorem? How do we separate out effective consistent first-order theories that do not have computable models?
Also, it is true that classical (Boolean) logic are not the only logic. There are infinitely many logics, below and above classical propositional logic. But this cannot be used to criticize the use of classical logic in some domain.
OK. My thought here was to show that classical (Boolean) logic is not unique and should not be taken as absolute. To do so would be a mistake similar to Kant's claim that Euclidean logic was absolute.
All treatises on any non classical logic used classical (or much more rarely intuitionistic) logic at the meta-level. You will not find a book on fuzzy logic having fuzzy theorems, for example. Non classical logics have multiple use, which are not related with the kind of ontic truth we are looking for when searching a TOE.
Of course fuzzy logic does not have fuzzy theorem, that could be mistaking the meaning of the word "fuzzy" with the meaning of the word "ambiguous". I have been trying to establish the validity of the idea that it is the rules (given as axioms, etc) that are used to define a given mathematical structure, be it a model, or an algebra, etc. But I think that one must be careful that the logical structure that one uses of a means to define ontic truths is not assumed to be absolute unless very strong reasons can be proven to exist for such assumptions.
Usually non classical logic have epistemic or pragmatic classical interpretations, or even classical formulation, like the classical modal logic S4 which can emulate intuitionistic logic, or the Brouwersche modal logic B, which can emulate weak quantum logic. This corresponds to the fact that intuitionist logic might modelize constructive provability, and quantum logic modelizes observability, and not the usual notion of classical truth (as used almost everywhere in mathematics).
I use the orthocomplete lattices as a representation of quantum logic. My ideas are influenced by the work of Svozil, Calude and von Benthem, and others on this. I am not sure of the definition of "weak quantum logic" as you use it here.
One question regarding the emulations. If one where considering only finite emulations of a quantum logic (such as how a classical approximation of a QM system could be considered), how might one apply the Tychonoff, Heine–Borel definition or Bolzano–Weierstrass criterion of compactness to be sure that compactness obtain for the models? If we use these compactness criteria, is it necessary that the collection of open sets that is used in complete in an absolute sense? COuld it be that we have a way to recover the appearence of the axiom of choice or the ultrafilter lemma?
Could it be possible to have a notion of accessibility to parametrize or weaking the word "every" as in the sentence: " A point x in X is a limit point of S if every open set containing x contains at least one point of S different from x itself." to "A point x in X is a limit point of S if every open set , that is assessible from some S, containing x contains at least one point of S different from x itself. The idea is that S and x cannot be an infinite distance (or infinite disjoint sequence of open sets) apart.
It seems to me that this would limit the implied omniscience of the compactness criteria (via the usual axiom of choice) and it seems more consistent with the notion that an emulation does not need to be *exact* to be informative.
To invoke the existence of non classical logic to throw a doubt about the universal truth of elementary statements in well defined domain, like arithmetic, would lead to complete relativism, given that you can always build some ad hoc logic/theory proving the negation of any statement, and this would make the notion of truth problematic. The contrary is true.
Relativism of that kind would be that last conclusion that I would desire! OTOH, we do need a clear notion of contextuality as illustrated by the way that words are defined in relation to other words in a dictionary.
A non classical logic is eventually accepted when we can find an interpretation of it in the classical framework.
This seems to be an unnecessary prejudice! Why is the classical framework presumed to be the absolute measure of acceptability and, by implication, Reality? This statement seems to reveal an explanation of why you believe that QM is derivative of classical logic somehow in spite of my repeated statements to the work of others that show that this is simply not possible except in a crude and non-faithful manner!
A non standard truth set, like the collection of open subsets of a topological space, provided a classical sense for intuitionist logic, like a lattice of linear subspaces can provide a classical interpretation of quantum logic (indeed quantum logic is born from such structures). It might be that nature observables obeys quantum logic, but quantum physicists talk and reason in classical logic, and use classical mathematical tools to describe the non classical behavior of matter.
I agree but will point out that the use of classical logic could be merely a habit and convenience. I think that there may be a reason why classical logics are taken as fundamental, but this reasoning is build on the intuition that a 3p "public" notion of communication can only be defined in Boolean logical terms; in other words, we observe a classical reality because that is the manner that maximally consistent collections of open sets can bisimulate each other. Bisimulation is communication between and within logical systems. If bisimulation cannot occur between a pair of logics then there is no interactions between the topological spaces dual to those logics. This gives us a way to think of seperate physical worlds. But this reasoning requires that we treat logics and topological spaces on an equal ontological footing. Logic cannot be taken as the unique ontological aspect of existence.
Onward!
Stephen
Bruno
http://iridia.ulb.ac.be/~marchal/
Bruno Marchal
On 28 Sep 2011, at 05:44, Pierz wrote:
> OK, well I think this and the other responses (notably Jason's) have
> brought me a lot closer to grasping the essence of this argument. I
> can see that the set of integers is also the set of all possible
> information states, and that the difference between that and the UD is
> the element of sequential computation. I can also see that my
> objection to infinite computational resources and state memory comes
> from the 1-p perspective. For me, in the "physical" universe, any
> computation is restricted by the laws of matter and must be embedded
> in that matter. Now one of the fascinating revelations of the
> computational approach to physics is the fact that a quantity such as
> position can only be defined to a certain level of precision by the
> universe itself because the universe has finite informational
> resources at its disposal. This was my objection to the UD. But I can
> see that this restriction need not necessarily apply at the 'higher'
> 3-
> p level of the UD's computations. What interests me is the question:
> does UDA predict that the 1-p observer will see a universe with such
> restrictions?
To be sure, this is an open problem.
To be sure, this is an open problem for physicists too.
Comp+"theatetus" will be refuted if the comp-physics will be quasi
*contradicted* by some precise physical fact, not by any physical
theory (unless they predicts that precise physical fact).
> If it explains why the 1-p observer seems to exist in a
> world where there is only a finite number of bits available, despite
> existing in a machine with an infinite level of bit resolution, then
> that would be a most interesting result. Otherwise, it seems to me to
> remain a problem for the theory, or at least a question in need of an
> answer, like dark matter in cosmology.
>
> I am going to have to meditate further on arithmetical realism. I
> don't believe in objective matter either (it seems refuted by Bell's
> Theorem anyway), but a chasm seems to lie between the statement "17
> is prime" and "the UDA (Robinson arithmetic) executes all possible
> programs".
Don't confuse the UD (Universal Dovetailer, a finite program) and UDA
(the UD Argument = the argument that, assuming digital mechanism,
physics is in principle a branch of number theory/computer science,
and in which the UD plays the role of the effective definable comp
ontological realm of *everything*).
Just a vocabulary remark, to avoid possible future confusion.
> The problem is one of instantiation. I can conceive of a
> universe - a singularity perhaps, with only one bit of information -
> in which the statement "17 is prime" can never be made.
Don't confuse the sociological statement "some machine asserts "17 is
prime"", and the true fact that 17 is prime, which does not rely on
physical universes at all, a priori.
> To formulate,
> ie instantiate, 17, requires a certain amount of information.
In some physical theory, but this is not an assumption in the theory.
You cannot refute an argument by adding new assumptions.
> To say
> that a program executes, as opposed to saying it merely is implied by
> a set of theoretical axioms, requires the instantiation of that
> algorithm.
In Aristotelian metaphysics.
Also, even in platonia, a computation is described by a big number
(possibly infinite) of implications.
> I suppose this is a restatement of the problem above.
> Arithemetical realism then would be the postulate that everything
> implied in arithmetic is actually instantiated.
Not at all. That would be a physicalist revisionist definition of
numbers. You need to "instantiate" 17, in some way, to talk about 17,
but 17 itself does not need instantiation. With or without any
physical universe, 17 remain a prime number.
Now, an instanciation, or emulation, can be defined from the numbers
alone. Some numbers are universal (a relative arithmetical property)
and we can say that a universal numbers instantiates 17 (say) if 17
appears in some of its purely arithmetical register.
To understand the detail of this, I can only refer you to some good
textbook in computer science. The main theorem for this is the proof
that all partial recursive functions can be represented in Robinson
arithmetic (Boolos and Jeffrey's book do this very well, Epstein and
carnielli also. ref in my theses).
> It seems to me I can
> grant 17 is prime, without granting this instantiation of everything.
Well, that solves you of a very long and not so easy work.
>
> I'm also troubled by the statement that you have proved in the AUDA
> that any Lobian machine can apprehend the UDA. Is not a three-year-old
> child and a cat a Lobian machine? Or indeed my senile father. How can
> you assert they could comprehend such an abstraction? Either they
> aren't Lobian machines, or there's hole in the proof somewhere,
> surely!
Recently I have updated my spectrum of Löbian machine to the octopus,
and the jumping spider. I can argue that they have the cognitive
ability to get UDA. But they don't have a sufficiently big brain to
exploit this, and they don't have the motivation to use diaries and
books, and language to generate their infinite "turing tape memory"
like we do.
Symptoms of Löbianity are believe in repetition and notice them (like
believing in a notion of anniversary), or having empathy for an other
creature, etc. This needs some form of the induction axiom. Robinson
arithmetic (and Universal machines in general) are not Löbian. Peano
Arithmetic is Löbian (it is reallu just Robinson arithmetic + the
induction axiom for the first order describable formula).
But this is not important for the reasoning.
>
> Jason mentions the anthropic principle (which of course I'm well
> acquainted with) and the idea of the computations which contain
> observers. I have read, without following, some of your propositions
> involving the Beweisbar predicate and self-referential relations and
> what have you. Is that the formalism that is supposed to define which
> computations are conscious?
Not really. This is a subtle point. Notion like truth and
consciousness are not definable by any machine. But, like with God (or
Plotnus' one) we, the machines, can talk in indirect way, by taking
some precaution.
> Is there a summary somewhere?
It is explained in the second part of the sane04 paper. AUDA is "the
interview of the Lôbian universal machine"
> I am
> wondering how consciousness can possibly be an attribute of some
> computations and not others,
Let me be precise; consciousness is not an attribute of a computation,
but is an attribute of a person. Now a person can manifest itself
relatively to other person, once "enough" similar computations are
going through the states of the two person, in some sufficiently
cohesive way. The self-reference logics are used to single out the
conditions of cohesion (unlike in linear logic, or Girard geometry of
interaction, which extract such condition from symmetry intuition and
proof theory).
> and why, if it's a matter of some certain
> mathematical properties of the computations, we could not fairly
> easily write a conscious algorithm?
It is easy. I tend to think, since recently, that all universal
algorithm are conscious. But their consciousness is disconnected, a
bit like if they were born ... in salvialand! And, yes, before doing
salvia I would have imposed Löbianity for consciousness, but I am much
less sure about that.
Now Löbianity is more than consciousness, it is self-consciousness.
Peano arithmetic is self-conscious, I think. That is why we can
discuss Plotinian theology with them, even without making their soul
falling on earth, that is without implementing them and sharing our
long story. Current computers have not yet long term memory, nor long
term goal. But I think that PA, the octopus, and the jumping spider
(but not worms, and most usual spider) are as conscious as you and me.
For the fun here is video illustrating that a jumping spider can do
some inductive inference requiring some implicit beliefs in
arithmetical induction (look hw she reacts when she looks behind the
mirror).
http://www.youtube.com/watch?v=iND8ucDiDSQ
As opposed, here is a typical non Löbian behavior, or a non jumping
spider (yet jumping, note):
http://www.youtube.com/watch?v=lsqt2ywSqTQ&feature=channel_video_title
If not finding food on a top of a plant, she is programmed to jump
randomly on other plant, and, in case she get the ground, to climb on
a nearest plant. Here there is only a pen, perpendicularly installed
on a flat ground table. She seems to repeat in cycle that behavior,
except for taking some rest.
But the bigger reason why I think jumping spiders are Löbian, is that
like cat and dog, they can bond with you, star at you, and perhaps
even recognize you. But this can be judged only by real interaction
with real spiders, not by looking at videoas, of course. Stiil, here
is a very cute one:
http://www.youtube.com/watch?v=MQBAIud6Twg&feature=related
> Surely complexity can't be the
> defining feature (at what arbitrary level of complexity does the light
> come on?), so it should be a simple matter.
I agree. You don't need more than 10 lines instruction code for them,
well, in a high logical language like prolog, for example.
> (Though the proof of
> having created consciousness in the program would be a problem!)
It is not a problem. It is an impossibility. You cannot prove that *I*
am conscious, can you?
> Don't
> we have to define consciousness (not necessarily self-awareness, or
> the awareness of being aware) as a property of numbers per se?
A quasi-definition is the ability by some universal numbers to
discover some non communicable truth by introspection. Consciousness
is not much more than the state of believing in some reality.
>
> Sadly when you start to talk about the difficulty of proving that our
> histories in the UD are more random than the actual histories we
> observe, I can't follow you any more - too much theory I'm unfamiliar
> with. I can see however that many (nearly all) of the infinite
> computations passing through our aware states will destroy us,
Gosh! I don't see that. ... Ah, you mean in a third person way. OK.
> as it
> were, so we can never exist in those computations (sort of anthropic
> principle). This also suggests a kind of immortality,
OK. This has been a recurrent theme on this list.
> the same kind as
> I propose in a blog post I wrote called the 'cryogenic paradox' in
> which I argue that there can only be a single observer, a single locus
> of consciousness underlying all apparently separate consciousnesses,
> which would really be just different perspectives of this one
> observer.
Nice. I agree with this, although it is not part of the reasoning. But
it makes the reasoning and comp fitting quite well with some aspect of
the salvia experience. Many mystics, including the greeks, thought in
that way. Ramana Maharsi too.
> It seems irresistible as a conclusion (from philosophical
> arguments quite different to the UDA), and yet also kind of horrific.
> Only a sort of state-bound recall barrier prevents us from being aware
> that we suffer every fate possible.
Yes. It is a bit frightening. It heals the fear of death, but can
expand the possible fear of life.
>
> I agree re academia. From all I can observe, it is a viper's pit. The
> ground of accepted truth is fought over as hard as any piece of the
> Holy Land, and in this as in all struggles, power matters. It is
> hardly the free and unbiased exchange between equal and curious minds!
> We are not so different today from the cardinals who refused to look
> down Galileo's telescope.
To be sure Galileo makes the big mistake too, in pretending that the
church was wrong and that he was right. He should have simply
pretended that his theory was more plausible, and more economical,
like the Church asked. But I see and follow your point.
>
> Finally, I despise all theory that makes obscurity a virtue. Compare
> Lacan's tedious impenetrability
Lacan was a great "humorist", except that its disciple did not
understand the joke, and Lacan falls in the idolatry trap.
In some seminar, he succeeded in being rather clear, and he said quite
genuine things on Gödel's theorem, which is rare.
Usually non-logicians say lot of crap on Gödel's results. Lacan and
Hofstadter are rather exceptions here.
But I think you are right, some text of Lacan were voluntarily
obscure, and I think that the purpose was a real mockery of its
audience.
> with Einstein's almost childish
> simplicity and profundity.
Sure.
> Obscurity is the darkness which merely
> clever minds use to cover their nakedness (to invoke the emperor
> again). No insult to you, Bruno, intended, this time.
We have to be a little cautious here. Even Einstein said that God was
simple but not that simple (I forget the exact quote). And the unknown
is obscure, quasi by definition, and with mechanism, we can explain
why some part have to remain obscure. But then this motivates the
honest researcher to be even more simple and clear. Obscurity should
not be a tool to hide ignorance (or more sinister intentions). Yet,
obscurity, in some field, cannot either been brushed away by pure
willing. That would be sort of wishful thinking.
Bruno
Pierz
> numbers. You need to "instantiate" 17, in some way, to talk about 17,
> but 17 itself does not need instantiation. With or without any
> physical universe, 17 remain a prime number.
a metaphysical assumption, not something that is provable. I would say
if you remove all minds, there is no 17, no primes, nothing, because
the numbers are lent existence by the mind and/or the physical
universe. My preferred ontology is idealistic (in the philosophical
sense) rather than mathematical. I tend to believe consciousness is
prior. And you've agreed consciousness can't really be defined - and
therefore dealt with explicitly in your theory. I believe there is a
pure conscious state somewhere down there (in us) that comes before
everything else, before the structure which is required to give form
to mathematics. Buddhism, the void, all that.
> > It seems to me I can
> > grant 17 is prime, without granting this instantiation of everything.
>
> Well, that solves you of a very long and not so easy work.
unless, like you, we make a living out of it! Otherwise we'd have to
prove our own arses before we could shit. But OK, this is profound
stuff, so what "seems to me" may be way off, on deeper investigation.
> Now, an instanciation, or emulation, can be defined from the numbers
> alone
instantiated emulation and the definition of the emulation aren't the
same. But I do understand what you are arguing (I think). There's
nothing intrinsically illogical about granting numbers an existence
that is prior to the physical or the mental, but are you claiming it's
*provable*?
> Recently I have updated my spectrum of Löbian machine to the octopus,
> and the jumping spider. I can argue that they have the cognitive
> ability to get UDA.
in theory, but it's kind of meaningless I think, since psychology
shows abstract reasoning is confined to humans above a certain age.
Still, I like the socratic octopus so much I'll believe you anyway.
I love the way the jumping spider literally falls off its perch when
there's no spider on the other side of the mirror. :)
> It is not a problem. It is an impossibility. You cannot prove that *I*
> am conscious, can you?
Finally, as for obscurity, I rejected obscurity treated as a virtue,
not the necessary obscurity of certain difficult ideas - like QFT
mathematics. I suppose jumping spiders can do QFT equations too,
right?
>
> read more »
Bruno Marchal
On 28 Sep 2011, at 15:53, Pierz wrote:
>> At what point does mathematical truth stop? It seems to be the
> existence of
>> some would imply the existence of all.
>
> Like I said, I need to let this marinate in my consciousness a while.
> I agree that all mathematical constructs must have the same kind of
> existence, the same ontological status. But I see a distinction
> between the type of existence pi has, and the type of existence that
> time, space and matter have. Well, obviously. The question is, are
> they prior to such instantiated entities, or emergent from them?
> Similar to the question, are physical laws objectively extant, or mere
> descriptions of 'habits'?
>
>> Do you agree that at least something has to be primitively real?
>
> Well I can't really escape that, can I? :) I favour consciousness as a
> prior reality, a spiritual position I suppose, though I also believe
> these categories may well just be prejudices in our mental make-up.
> For physicists, it's the quantum field, for mathematicians it's
> number, for saints it is love. All perhaps faces of an unnameable
> prior something. I've read Bruno arguing for number's capacity to
> explain qualia, and I find it unconvincing.
Do you mean by this that you think that we are not machine?
Are you rejecting Theaetetus theory of knowledge (true opinion)?
What is not convincing?
> Mathematics is pure
> structure and qualia are non structural, non quantifiable, not that
> they are 'uncomputable', but just don't fall into the computable/
> uncomputable opposition at all.
Modal logic is both mathematics, and it handle the non-computable, and
the qualitative.
In particular some of the variant of self-reference modal logic handle
explicitly and in a formal way the knowledge that the machine itself
is unable to formalise. It is (meta) formal logic of the non
formalisable.
> If a person had no right brain at all,
> he might argue the way Bruno does on this point. (I'm worried about
> insulting him again now. I don't mean it's half brained. I mean it is
> blind to all but the quantifiable, and therefore will never satisfy an
> artist, for instance).
Those who have the less problem with mechanism and its consequences
are the artists and the engineers.
> So qualia make me prefer to seek my ontological
> roots in the notion of consciousness rather than number.
This is frequent with mystically inclined people, but I think it is
just due to a reductionist conception of numbers and machines, which
is provably untenable since Gödel's discovery of incompleteness. You
are the one dismissing qulaia for a vast type of entity, in case you
use this to refute mechanism.
>
>> We also are aware of every possible goodness or blessing. At a
>> minimum,
>> this realization should compel us to treat each other better. In
>> the end,
>> the conclusion is little different from the golden rule or the
>> concept of
>> karma. All the good things we do are experienced by others
>> (ourselves),
>> same with all the bad things.
>
> Yes, yes and double yes. I made the exact same point in that blog post
> I mentioned on the subject. If we knew this, truly believed in this
> unity of the observer, we would move quick smart to a society
> optimized for the benefit of all. We can never gain at another's
> expense. Not "There but for the grace of God go I" but simply "There
> go I."
OK. But this is non communicable by (sound) machines. In fact in the
ethics of the ideally correct machine, asserting moral principle is
immoral. We can only encourage people to understand or discover this
by themselves.
Bruno
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Bruno Marchal
On 29 Sep 2011, at 04:11, Pierz wrote:
>> Not at all. That would be a physicalist revisionist definition of
>> numbers. You need to "instantiate" 17, in some way, to talk about 17,
>> but 17 itself does not need instantiation. With or without any
>> physical universe, 17 remain a prime number.
>
> With or without a mind too, I presume you believe. But this really is
> a metaphysical assumption,
No, it is mathematical practice. When numbers are introduced in high
school they are not defined by referring to mind or brain, which are
more complex notion.
> not something that is provable.
Axioms are never provable, except in redundant theories (for making
them easier to use).
> I would say
> if you remove all minds, there is no 17, no primes, nothing, because
> the numbers are lent existence by the mind and/or the physical
> universe.
Mechanism makes mind definable from numbers, but nobody has succeeded
in defining numbers from mind, without using numbers.
> My preferred ontology is idealistic (in the philosophical
> sense) rather than mathematical. I tend to believe consciousness is
> prior. And you've agreed consciousness can't really be defined - and
> therefore dealt with explicitly in your theory.
We cannot define consciousness, nor truth, etc. but we do have a good
idea of what those things refer too.
> I believe there is a
> pure conscious state somewhere down there (in us) that comes before
> everything else, before the structure which is required to give form
> to mathematics. Buddhism, the void, all that.
We might be close, we can equivocate numbers and consciousness in
different ways. Do you say "yes" to the doctor?
(It looks like entheogen.com is out of line currently. Hope it will
coma back!).
>
>>> It seems to me I can
>>> grant 17 is prime, without granting this instantiation of
>>> everything.
>>
>> Well, that solves you of a very long and not so easy work.
>
> Haha. Well, thank god we don't have to prove everything we believe -
> unless, like you, we make a living out of it! Otherwise we'd have to
> prove our own arses before we could shit. But OK, this is profound
> stuff, so what "seems to me" may be way off, on deeper investigation.
Arithmetical truth is full of currently non human provable truth
(unless we have actual infinite brains, which I doubt).
>
>> Now, an instanciation, or emulation, can be defined from the numbers
>> alone
>
> I can believe that without the textbook. I'm just saying that the
> instantiated emulation and the definition of the emulation aren't the
> same.
You can define emulation in arithmetic, that is one thing. But you can
prove that arithmetic is full of instantiated emulations. That is the
thing explained in textbook I was referring too. If comp is true, you
are conscious here and now, because an infinity of number relation
emulate your computational histories.
> But I do understand what you are arguing (I think). There's
> nothing intrinsically illogical about granting numbers an existence
> that is prior to the physical or the mental, but are you claiming it's
> *provable*?
This is provable assuming you can survive with a material digital
brain. That is comp, and comp is not provable.
>
>> Recently I have updated my spectrum of Löbian machine to the octopus,
>> and the jumping spider. I can argue that they have the cognitive
>> ability to get UDA.
>
> I just find that quite funny. The socratic octopus. You can argue it
> in theory, but it's kind of meaningless I think, since psychology
> shows abstract reasoning is confined to humans above a certain age.
Conscious high level abstract reasoning is such confined, but all
brain of all animals does "abstract reasoning" all the time. Seeing
the difference between vertical and horizontal line require complex
computations in the brain.
> Still, I like the socratic octopus so much I'll believe you anyway.
> I love the way the jumping spider literally falls off its perch when
> there's no spider on the other side of the mirror. :)
Yes, that shows she makes inductive inference, which requires her to
be Löbian. Insects seems unable to do this.
>
>> It is not a problem. It is an impossibility. You cannot prove that
>> *I*
>> am conscious, can you?
>
> No of course not, that's what I meant by a "problem". A very big one!
No, that is not a problem. Since Gödel we know that all machine are
confronted with many unprovable truth.
>
> Finally, as for obscurity, I rejected obscurity treated as a virtue,
> not the necessary obscurity of certain difficult ideas - like QFT
> mathematics. I suppose jumping spiders can do QFT equations too,
> right?
They don't have a sufficiently big brain to handle the motivations for
it. But they can in principle. A bit like a baby, except that a baby
can develop better its brain than such little animals.
Bruno
Bruno Marchal
On 9/27/2011 10:47 AM, Bruno Marchal wrote:
On 27 Sep 2011, at 13:49, Stephen P. King wrote:
On 9/26/2011 7:56 PM, Jason Resch wrote:
<snip>
For well-defined propositions regarding the numbers I think the values are confined to true or false.[SPK]
Jason
--
Not in general, unless one is only going to allow only Boolean logics to exist. There have been proven to exist logics that have truth values that range over any set of numbers, not just {0,1}. Recall the requirement for a mathematical structure to exist: Self-consistency.
Consistency is a notion applied usually to theories, or (chatty) machines, not to mathematical structures.
A theory is consistent if it does not prove some proposition and its negation. A machine is consistent if it does not assert a proposition and its negation.
[SPK]
Is not a machine represented mathematically by some abstract (mathematical ) structure? I am attempting to find clarity in the ideas surrounding the notion of "machine" and how you arrive at the idea that the abstract notion of implementation is sufficient to derive the physical notion of implementation.
In first order logic we have Gödel-Henkin completeness theorem which shows that a theory is consistent if and only if there is a mathematical structure (called model) satisfying (in a sense which can be made precise) the proposition proved in the theory.
[SPK]
What constraints are defined on the models by the Gödel-Henkin completeness theorem? How do we separate out effective consistent first-order theories that do not have computable models?
[SPK]
Also, it is true that classical (Boolean) logic are not the only logic. There are infinitely many logics, below and above classical propositional logic. But this cannot be used to criticize the use of classical logic in some domain.
OK. My thought here was to show that classical (Boolean) logic is not unique and should not be taken as absolute. To do so would be a mistake similar to Kant's claim that Euclidean logic was absolute.
All treatises on any non classical logic used classical (or much more rarely intuitionistic) logic at the meta-level. You will not find a book on fuzzy logic having fuzzy theorems, for example. Non classical logics have multiple use, which are not related with the kind of ontic truth we are looking for when searching a TOE.
[SPK]
Of course fuzzy logic does not have fuzzy theorem, that could be mistaking the meaning of the word "fuzzy" with the meaning of the word "ambiguous". I have been trying to establish the validity of the idea that it is the rules (given as axioms, etc) that are used to define a given mathematical structure, be it a model, or an algebra, etc. But I think that one must be careful that the logical structure that one uses of a means to define ontic truths is not assumed to be absolute unless very strong reasons can be proven to exist for such assumptions.
Usually non classical logic have epistemic or pragmatic classical interpretations, or even classical formulation, like the classical modal logic S4 which can emulate intuitionistic logic, or the Brouwersche modal logic B, which can emulate weak quantum logic. This corresponds to the fact that intuitionist logic might modelize constructive provability, and quantum logic modelizes observability, and not the usual notion of classical truth (as used almost everywhere in mathematics).
[SPK]
I use the orthocomplete lattices as a representation of quantum logic. My ideas are influenced by the work of Svozil, Calude and von Benthem, and others on this. I am not sure of the definition of "weak quantum logic" as you use it here.
One question regarding the emulations. If one where considering only finite emulations of a quantum logic (such as how a classical approximation of a QM system could be considered), how might one apply the Tychonoff, Heine–Borel definition or Bolzano–Weierstrass criterion of compactness to be sure that compactness obtain for the models? If we use these compactness criteria, is it necessary that the collection of open sets that is used in complete in an absolute sense? COuld it be that we have a way to recover the appearence of the axiom of choice or the ultrafilter lemma?
Could it be possible to have a notion of accessibility to parametrize or weaking the word "every" as in the sentence: " A point x in X is a limit point of S if every open set containing x contains at least one point of S different from x itself." to "A point x in X is a limit point of S if every open set , that is assessible from some S, containing x contains at least one point of S different from x itself. The idea is that S and x cannot be an infinite distance (or infinite disjoint sequence of open sets) apart.
It seems to me that this would limit the implied omniscience of the compactness criteria (via the usual axiom of choice) and it seems more consistent with the notion that an emulation does not need to be *exact* to be informative.
[SPK]
To invoke the existence of non classical logic to throw a doubt about the universal truth of elementary statements in well defined domain, like arithmetic, would lead to complete relativism, given that you can always build some ad hoc logic/theory proving the negation of any statement, and this would make the notion of truth problematic. The contrary is true.
Relativism of that kind would be that last conclusion that I would desire! OTOH, we do need a clear notion of contextuality as illustrated by the way that words are defined in relation to other words in a dictionary.
A non classical logic is eventually accepted when we can find an interpretation of it in the classical framework.{SPK]
This seems to be an unnecessary prejudice! Why is the classical framework presumed to be the absolute measure of acceptability and, by implication, Reality?
This statement seems to reveal an explanation of why you believe that QM is derivative of classical logic somehow in spite of my repeated statements to the work of others that show that this is simply not possible except in a crude and non-faithful manner!
[SPK]
A non standard truth set, like the collection of open subsets of a topological space, provided a classical sense for intuitionist logic, like a lattice of linear subspaces can provide a classical interpretation of quantum logic (indeed quantum logic is born from such structures). It might be that nature observables obeys quantum logic, but quantum physicists talk and reason in classical logic, and use classical mathematical tools to describe the non classical behavior of matter.
I agree but will point out that the use of classical logic could be merely a habit and convenience.
I think that there may be a reason why classical logics are taken as fundamental, but this reasoning is build on the intuition that a 3p "public" notion of communication can only be defined in Boolean logical terms; in other words, we observe a classical reality because that is the manner that maximally consistent collections of open sets can bisimulate each other. Bisimulation is communication between and within logical systems. If bisimulation cannot occur between a pair of logics then there is no interactions between the topological spaces dual to those logics. This gives us a way to think of seperate physical worlds. But this reasoning requires that we treat logics and topological spaces on an equal ontological footing. Logic cannot be taken as the unique ontological aspect of existence.
Stephen P. King
>> Not at all. That would be a physicalist revisionist definition of
>> numbers. You need to "instantiate" 17, in some way, to talk about 17,
>> but 17 itself does not need instantiation. With or without any
>> physical universe, 17 remain a prime number.
> With or without a mind too, I presume you believe. But this really is
> a metaphysical assumption, not something that is provable. I would say
> if you remove all minds, there is no 17, no primes, nothing, because
> the numbers are lent existence by the mind and/or the physical
> universe. My preferred ontology is idealistic (in the philosophical
> sense) rather than mathematical. I tend to believe consciousness is
> prior. And you've agreed consciousness can't really be defined - and
> therefore dealt with explicitly in your theory. I believe there is a
> pure conscious state somewhere down there (in us) that comes before
> everything else, before the structure which is required to give form
> to mathematics. Buddhism, the void, all that.
I would disagree with this claim. There is a difference between the
existence on an entity and its properties and the definiteness thereof.
Existence and the property of having a definite set of properties (as
opposed to having a spectrum of possible properties) should not be
conflated. My reasoning is that if the existence of an entity where to
depend on whether or not a mind has the object as a subject of
perception or a physical entity has some other as a effective cause of
some property of its own then existence would be a property that an
object could have. Is existence a property that we measure, even in
principle? No.
Why is this conflation so rampant in thought? I have even seen
instances of this kind of language in the work of the estimable David
Deutsch! How is even the question of "does the existence of an entity
depend on its perception by some other entity" not seen instantly as
oxymoronic?
>>> It seems to me I can
>>> grant 17 is prime, without granting this instantiation of everything.
>> Well, that solves you of a very long and not so easy work.
> Haha. Well, thank god we don't have to prove everything we believe -
> unless, like you, we make a living out of it! Otherwise we'd have to
> prove our own arses before we could shit. But OK, this is profound
> stuff, so what "seems to me" may be way off, on deeper investigation.
[SPK]
Could it be that the definiteness of properties of our arses, in
this example, are something that is contingent on interactions but not
the possibility of having properties is not?
>> Now, an instanciation, or emulation, can be defined from the numbers
>> alone
> I can believe that without the textbook. I'm just saying that the
> instantiated emulation and the definition of the emulation aren't the
> same. But I do understand what you are arguing (I think). There's
> nothing intrinsically illogical about granting numbers an existence
> that is prior to the physical or the mental, but are you claiming it's
> *provable*?
[SPK]
To elaborate on this question by Pierz, is not "provability" a
property that must be demonstrated to occur for a given abstract entity?
>> Recently I have updated my spectrum of L�bian machine to the octopus,
>> and the jumping spider. I can argue that they have the cognitive
>> ability to get UDA.
> I just find that quite funny. The socratic octopus. You can argue it
> in theory, but it's kind of meaningless I think, since psychology
> shows abstract reasoning is confined to humans above a certain age.
> Still, I like the socratic octopus so much I'll believe you anyway.
> I love the way the jumping spider literally falls off its perch when
> there's no spider on the other side of the mirror. :)
[SPK]
It would be interesting to see the experiment that would allow us
to determine whether or not an octopus or spider can distinguish between
a purely abstract concept and the actuality of a physical entity. How do
we determine that a spider has thoughts about its percepts?
>> It is not a problem. It is an impossibility. You cannot prove that *I*
>> am conscious, can you?
> No of course not, that's what I meant by a "problem". A very big one!
>
> Finally, as for obscurity, I rejected obscurity treated as a virtue,
> not the necessary obscurity of certain difficult ideas - like QFT
> mathematics. I suppose jumping spiders can do QFT equations too,
> right?
[SPK]
How could we determined If they can know that what they are doing
is QFT even if they can solve QFT equations?
Onward!
Stephen
>> Recently I have updated my spectrum of L�bian machine to the octopus,
>> and the jumping spider. I can argue that they have the cognitive
>> ability to get UDA. But they don't have a sufficiently big brain to
>> exploit this, and they don't have the motivation to use diaries and
>> books, and language to generate their infinite "turing tape memory"
>> like we do.
>> Symptoms of L�bianity are believe in repetition and notice them (like
>> believing in a notion of anniversary), or having empathy for an other
>> creature, etc. This needs some form of the induction axiom. Robinson
>> arithmetic (and Universal machines in general) are not L�bian. Peano
>> Arithmetic is L�bian (it is reallu just Robinson arithmetic + the
>> induction axiom for the first order describable formula).
>> But this is not important for the reasoning.
>>
>>
>>
>>> Jason mentions the anthropic principle (which of course I'm well
>>> acquainted with) and the idea of the computations which contain
>>> observers. I have read, without following, some of your propositions
>>> involving the Beweisbar predicate and self-referential relations and
>>> what have you. Is that the formalism that is supposed to define which
>>> computations are conscious?
>> Not really. This is a subtle point. Notion like truth and
>> consciousness are not definable by any machine. But, like with God (or
>> Plotnus' one) we, the machines, can talk in indirect way, by taking
>> some precaution.
>>
>>> Is there a summary somewhere?
>> It is explained in the second part of the sane04 paper. AUDA is "the
>> interview of the L�bian universal machine"
>>
>>> I am
>>> wondering how consciousness can possibly be an attribute of some
>>> computations and not others,
>> Let me be precise; consciousness is not an attribute of a computation,
>> but is an attribute of a person. Now a person can manifest itself
>> relatively to other person, once "enough" similar computations are
>> going through the states of the two person, in some sufficiently
>> cohesive way. The self-reference logics are used to single out the
>> conditions of cohesion (unlike in linear logic, or Girard geometry of
>> interaction, which extract such condition from symmetry intuition and
>> proof theory).
>>
>>> and why, if it's a matter of some certain
>>> mathematical properties of the computations, we could not fairly
>>> easily write a conscious algorithm?
>> It is easy. I tend to think, since recently, that all universal
>> algorithm are conscious. But their consciousness is disconnected, a
>> bit like if they were born ... in salvialand! And, yes, before doing
>> salvia I would have imposed L�bianity for consciousness, but I am much
>> less sure about that.
>> Now L�bianity is more than consciousness, it is self-consciousness.
>> Peano arithmetic is self-conscious, I think. That is why we can
>> discuss Plotinian theology with them, even without making their soul
>> falling on earth, that is without implementing them and sharing our
>> long story. Current computers have not yet long term memory, nor long
>> term goal. But I think that PA, the octopus, and the jumping spider
>> (but not worms, and most usual spider) are as conscious as you and me.
>>
>> For the fun here is video illustrating that a jumping spider can do
>> some inductive inference requiring some implicit beliefs in
>> arithmetical induction (look hw she reacts when she looks behind the
>> mirror).
>>
>> http://www.youtube.com/watch?v=iND8ucDiDSQ
>>
>> As opposed, here is a typical non L�bian behavior, or a non jumping
>> spider (yet jumping, note):
>>
>> http://www.youtube.com/watch?v=lsqt2ywSqTQ&feature=channel_video_title
>>
>> If not finding food on a top of a plant, she is programmed to jump
>> randomly on other plant, and, in case she get the ground, to climb on
>> a nearest plant. Here there is only a pen, perpendicularly installed
>> on a flat ground table. She seems to repeat in cycle that behavior,
>> except for taking some rest.
>>
>> But the bigger reason why I think jumping spiders are L�bian, is that
>> like cat and dog, they can bond with you, star at you, and perhaps
>> even recognize you. But this can be judged only by real interaction
>> with real spiders, not by looking at videoas, of course. Stiil, here
>> is a very cute one:
>>
>> http://www.youtube.com/watch?v=MQBAIud6Twg&feature=related
>>
>>> Surely complexity can't be the
>>> defining feature (at what arbitrary level of complexity does the light
>>> come on?), so it should be a simple matter.
>> I agree. You don't need more than 10 lines instruction code for them,
>> well, in a high logical language like prolog, for example.
>>
>>> (Though the proof of
>>> having created consciousness in the program would be a problem!)
>> It is not a problem. It is an impossibility. You cannot prove that *I*
>> am conscious, can you?
>>
>>> Don't
>>> we have to define consciousness (not necessarily self-awareness, or
>>> the awareness of being aware) as a property of numbers per se?
>> A quasi-definition is the ability by some universal numbers to
>> discover some non communicable truth by introspection. Consciousness
>> is not much more than the state of believing in ...
>>
>> read more �
Stephen P. King
On 28 Sep 2011, at 16:44, Stephen P. King wrote:
On 9/27/2011 10:47 AM, Bruno Marchal wrote:
On 27 Sep 2011, at 13:49, Stephen P. King wrote:
On 9/26/2011 7:56 PM, Jason Resch wrote:
<snip>
For well-defined propositions regarding the numbers I think the values are confined to true or false.
Jason
--�[SPK]
��� Not in general, unless one is only going to allow only Boolean logics to exist. There have been proven to exist logics that have truth values that range over any set of numbers, not just {0,1}. Recall the requirement for a mathematical structure to exist: Self-consistency.
Consistency is a notion applied usually to theories, or (chatty) machines, not to mathematical structures.
A theory is consistent if it does not prove some proposition and its negation. A machine is consistent if it does not assert a proposition and its negation.
[SPK]
��� Is not a machine represented mathematically by some abstract (mathematical ) structure?� I am attempting to find clarity in the ideas surrounding the notion of "machine" and how you arrive at the idea that the abstract notion of implementation is sufficient to derive the physical notion of implementation.
This follows from the UD Argument, in the digital mechanist theory. No need of AUDA or complex math to understand the necessity of this, once we accept that we can survive with (physical, material) digital machines.
[SPK]
��� Is the property of universality independent of whether or not a machine has a set of properties? What is it that determines the properties of a machine? I need to understand better your definition of the word "machine".
In first order logic we have G�del-Henkin completeness theorem which shows that a theory is consistent if and only if there is a mathematical structure (called model) satisfying (in a sense which can be made precise) the proposition proved in the theory.
[SPK]
��� What constraints are defined on the models by the G�del-Henkin completeness theorem? How do we separate out effective consistent first-order theories that do not have computable models?
What do you mean by computable models?
[SPK]
��� Allow me to quote several definitions: "computable functions are exactly the functions that can be calculated using a mechanical calculation device given unlimited amounts of time and storage space. " (from http://en.wikipedia.org/wiki/Computable_function).� "a computable model is one whose underlying set is decidable and whose functions and relations are uniformly computable. " (from http://arxiv.org/abs/math/0602483).
��� A computable model, as I understand it, could be considered as a representation of a system or structure whose properties can be determined by some process that can itself be represented as a function from the set of countable numbers to itself. This defintion seeks to abstractly represent the way that we can determine the properties of a physical system X or, equivalently, generate a finite list of operations that will create an instance of X.
[SPK]
Also, it is true that classical (Boolean) logic are not the only logic. There are infinitely many logics, below and above classical propositional logic. But this cannot be used to criticize the use of classical logic in some domain.
��� OK. My thought here was to show that classical (Boolean) logic is not unique and should not be taken as absolute. To do so would be a mistake similar to Kant's claim that Euclidean logic was absolute.
OK, but then why to use that fact to criticize Jason's defense of arithmetical truth independent of humans.
[SPK]
��� I am claiming a distinction between the existence of a structure and the definiteness of its properties. It is my claim that prior to the establishment of whether or not a method of determining or deciding what the properties of a structure or system are, one can only consider the possibility of the structure or system. For example, say some proposition or sentence of a language exists. Does that existence determine the particulars of that proposition or sentence? If it can how so? How do can we claim to be able to decide that P_i is true in the absence of a means to determine or decide what P_i means?
��� How do you know the meaning of these word "Unicorn"? Is the meaning of the word "Unicorn" something that that arises simply from the existence of sequence of symbols? is not meaning not something like a map between some set of properties instantiated entity and some set of instances of those properties in other entities? Consider an entity X that had a set of properties x_i that could not be related to those of any other entity? Would this prevent the existence of X?
The existence of X is the necessary possibility of X, []<>X.
All treatises on any non classical logic used classical (or much more rarely intuitionistic) logic at the meta-level. You will not find a book on fuzzy logic having fuzzy theorems, for example. Non classical logics have multiple use, which are not related with the kind of ontic truth we are looking for when searching a TOE.
[SPK]
��� Of course fuzzy logic does not have fuzzy theorem, that could be mistaking the meaning of the word "fuzzy" with the meaning of the word "ambiguous". I have been trying to establish the validity of the idea that it is the rules (given as axioms, etc) that are used to define a given mathematical structure, be it a model, or an algebra, etc. But I think that one must be careful that the logical structure that one uses of a means to define ontic truths is not assumed to be absolute unless very strong reasons can be proven to exist for such assumptions.
Usually non classical logic have epistemic or pragmatic classical interpretations, or even classical formulation, like the classical modal logic S4 which can emulate intuitionistic logic, or the Brouwersche modal logic B, which can emulate weak quantum logic. This corresponds to the fact that intuitionist logic might modelize constructive provability, and quantum logic modelizes observability, and not the usual notion of classical truth (as used almost everywhere in mathematics).
[SPK]
��� I use the orthocomplete lattices as a representation of quantum logic. My ideas are influenced by the work of Svozil, Calude� and von Benthem, and others on this. I am not sure of the definition of "weak quantum logic" as you use it here.
Svozil, Calude and van Benthem thought on the subject are very good. Weak quantum logic is the logic of sublattice of ortholattices, like in the paper of Goldblatt that I have often refer to you. Basically it is quantum logic without the orthomodularity axiom. It does not distinguish finite dimensional pre-Hilbert space from Hilbert space, for example.
[SPK]
��� This paper http://www.jstor.org/pss/2274172 ? It seems to me that the distributivity axiom would not make the same distinction either, although Hilbert space is defined in terms of a linear algebra on a vector space. Consider this paper's abstract.
http://www.google.com/url?sa=t&rct=j&q=orthomodularity%20axiom&source=web&cd=5&sqi=2&ved=0CDgQFjAE&url=http%3A%2F%2Fm3k.grad.hr%2Fpapers-ps-pdf%2Fquantum-logic%2F1998-helv-phys-acta.pdf&ei=N3SETo2yFYGztwfLiYU0&usg=AFQjCNHal3UDb6B-MATSt1hloWFhSNVCnw&sig2=Fl7ESJLpFZ9qj8c8YU8S-w&cad=rja
"We show that binary orthologic becomes either quantum or classical logic when nothing but modus
ponens rule is added to it, depending on the kind of the operation of implication used. We also show that
in the usual approach the rule characterizes neither quantum nor classical logic. The diff erence turns out
to stem from the chosen valuation on a model of a logic. Thus algebraic mappings of axioms of standard
quantum logics would fail to yield an orthomodular lattice if a unary - as opposed to binary - valuation
were used. Instead, non-orthomodular nontrivial varieties of orthologic are obtained. We also discuss the
computational efficiency of the binary quantum logic and stress its importance for quantum computation
and related algorithms."
��� How can we even consider the distinction of one form of abstract structure, such as logical algebras or lattices, from another without there existing a means to generate instantiations of the two? This question goes to the heart of my skepticism of your result.
[SPK]
��� One question regarding the emulations. If one where considering only finite emulations of a quantum logic (such as how a classical approximation of a QM system could be considered), how might one apply the Tychonoff, Heine�Borel definition or Bolzano�Weierstrass criterion of compactness to be sure that compactness obtain for the models? If we use these compactness criteria, is it necessary that the collection of open sets that is used in complete in an absolute sense? Could it be that we have a way to recover the appearence of the axiom of choice or the ultrafilter lemma?
Hard and premature questions.
��� But do we not decide whether or not to pursue a conjecture by the implications of the conjecture? The questions that I am asking here are questions of the ability of the idea to give us an explanatory narrative that we can use to reason about our world. You are, with your result, proposing a result that implies an ontological theory: that Reality is, at its primitive level, purely abstract. This seems to be more of an echo of the ideas of Pythagoras than those of Plato...
��� Could it be possible to have a notion of accessibility to parametrize or weaking the word "every" as in the sentence: " A point x in X is a limit point of S if every open set containing x contains at least one point of S different from x itself." to "A point x in X is a limit point of S if every open set , that is assessible from some S, containing x contains at least one point of S different from x itself. The idea is that S and x cannot be an infinite distance (or infinite disjoint sequence of open sets) apart.
��� It seems to me that this would limit the implied omniscience of the compactness criteria (via the usual axiom of choice) and it seems more consistent with the notion that an emulation does not need to be *exact* to be informative.
Perhaps. Cerrtainly open problem in comp+Theaetetus.
[SPK]
��� Does that not imply that the explanatory value of comp+Theaetus is partly dependent of the resolution of such a problem? If we are going to seriously consider your form of ideal monism to be correct, as opposed to some form of non-substance dualism or material monism or neutral monism, do such questions not need to be looked at with seriousness? I am very interested in ontological theories, thus my queries.
�
[SPK]
To invoke the existence of non classical logic to throw a doubt about the universal truth of elementary statements in well defined domain, like arithmetic, would lead to complete relativism, given that you can always build some ad hoc logic/theory proving the negation of any statement, and this would make the notion of� truth problematic. The contrary is true.
��� Relativism of that kind would be that last conclusion that I would desire! OTOH, we do need a clear notion of contextuality as illustrated by the way that words are defined in relation to other words in a dictionary.
I am problem driven. I start from the problem, and use the available math.
[SPK]
��� As am I. ;-) But I think that sometimes we need to look beyond the math and consider how it is that knowledge itself is possible.
A non classical logic is eventually accepted when we can find an interpretation of it in the classical framework.{SPK]
[SPK]��� This seems to be an unnecessary prejudice! Why is the classical framework presumed to be the absolute measure of acceptability and, by implication, Reality?
No. Simplicity. Together with the need of the classical Church thesis, and our intuition of numbers. We do use the comp hypothesis, and it needs classical logic on the natural numbers. Intuitionist logic can also be used, but then the math are much more complex, and eventually we need a non trivial use of the double negation topology. It is more easy to use, like usually in math, the meta-classical background.�
��� But it seems that you are assuming that our ability to have intuitions of abstractions itself has a satisfactory explanation. You seem to assume that the properties of, for example, memory obtain solely from the existence of Arithmetic and that such existence is severable from the physical instantiations of memory.
This statement seems to reveal an explanation of why you believe that QM is derivative of classical logic somehow in spite of my repeated statements to the work of others that show that this is simply not possible except in a crude and non-faithful manner!
You repeatedly confuse the notion of embedding of a logic in another, and representing a logic in another. I have explained this many times, but you keep coming back on that confusion. QL cannot be faithfully extended in Boolean logic, but this does not mean that you cannot represent QL in a classical frame work (like it is done all the time; quantum mechanics is itself a classical theory).
��� How is a representation of logic A in logic B not equivalent to an embedding of A in B? Maybe I am conflating a model with a representation.
[SPK]
A non standard truth set, like the collection of open subsets of a topological space, provided a classical sense for intuitionist logic, like a lattice of linear subspaces can provide a classical interpretation of quantum logic (indeed quantum logic is born from such structures). It might be that nature observables obeys quantum logic, but quantum physicists talk and reason in classical logic, and use classical mathematical tools to describe the non classical behavior of matter.
��� I agree but will point out that the use of classical logic could be merely a habit and convenience.
Classical logic allows non constructive reasoning which are obligatory in any modest theology, like the machine's theologies.Do you agree that a (mathematical) machine stop or ... do not stop, on some input. We don't need more than that.
[SPK]
��� A mathematical object, as I can understand it, is purely an abstraction that supervenes upon the actions of a mind to have a meaning. The particular properties of the object flow from the rules, axioms, etc. that are used to define said object and do not depend on anything else except the possibility of some instantiation of those rules, axioms, etc. If a "machine" is a form of mathematical structure then its existence is not predicated on any particular instantiation of such a machine but its properties are not defined by the mere possibility of its existence. Additionally, the notion of "stopping" or "not stopping" has a meaning that refers to a process in some way. A process cannot be reduced to a static relation between abstract entities but it can be represented by sequences of static relations. I distinguish between the representation of a process and the process itself. A map is not the territory.
��� OTOH, if we consider the idea that we can relate simulations of a given process with the process itself, we are comparing one form of process to another, not a static set of relations to a process. I do not think of mathematical objects as static relations only, I see them more as invariant patterns that occur in a background of eternal interactions between possible aspects of Existence.
I think that there may be a reason why classical logics are taken as fundamental, but this reasoning is build on the intuition that a 3p "public" notion of communication can only be defined in Boolean logical terms; in other words, we observe a classical reality because that is the manner that maximally consistent collections of open sets can bisimulate each other. Bisimulation is communication between and within logical systems. If bisimulation cannot occur between a pair of logics then there is no interactions between the topological spaces dual to those logics. This gives us a way to think of seperate physical worlds. But this reasoning requires that we treat logics and topological spaces on an equal ontological footing. Logic cannot be taken as the unique ontological aspect of existence.
It follows from the step 8 of UDA that if we are machine, classical arithmetic is a theory of everything. Non classical logics are recovered in the machine's epistemologies. S4grz1 is intuitionist and the Z1* and X1* logics are type of quantum logics.
��� If we are some abstract static relational structure then Arithmetic is an explanation of everything? Maybe for an abstract and static entity, but not for an entity that needs to explain the appearance of a universe that is never only identically itself. I do not identify an arbitrary collection of static relations with Change in a decidable one to one and onto way.
Onward!
Stephen
Stephen P. King
--Dear Bruno,
��� Please see the following paper for the kind of ideas that I am considering:
"Abstract. The fact that one can associate a finite monoid with universal
properties to each language recognized by an automaton is central to the
solution of many practical and theoretical problems in automata theory.
It is particularly useful, via the advanced theory initiated by Eilenberg
and Reiterman, in separating various complexity classes and, in some
cases it leads to decidability of such classes. In joint work with Jean-� Eric
Pin and Serge Grigorieff we have shown that this theory may be seen as
a special case of Stone duality for Boolean algebras extended to a duality
between Boolean algebras with additional operations and Stone spaces
equipped with Kripke style relations. This is a duality which also plays a
fundamental role in other parts of the foundations of computer science,
including in modal logic and in domain theory. In this talk I will give
a general introduction to Stone duality and explain what this has to do
with the connection between regular languages and monoids."
��� I am exploring the ontological, thus philosophical, implications of these ideas. My basic hypothesis is: If Abstract Objects exist then so too do Topological Spaces that act as the physical worlds that implement them. Reality is ontologically dual in that both abstract and concrete objects exist and are related to each other such that one cannot exist except if its dual also exists. Mind is an instance of an abstract dynamical process, the brain is a form of implementation of mind. Logics (including minds) and physical objects do not interact since they are necessary and dual forms of the same neutral grundlagen, the totality of existence in itself.
Ownard!
Stephen
meekerdb
> OK. But this is non communicable by (sound) machines. In fact in the ethics of the
> ideally correct machine, asserting moral principle is immoral. We can only encourage
> people to understand or discover this by themselves.
>
> Bruno
Several times you have made moral assertions (like the immoral one above :-) ), and I
have agreed with them. But I don't see how they follow from the UDA. An objective basis
of agreement on ethics and morals would be a great advance in world peace, so I'm very
interested in how you derive these assertions (which you shouldn't make).
Brent
Bruno Marchal
On 9/29/2011 4:03 AM, Bruno Marchal wrote:
On 28 Sep 2011, at 16:44, Stephen P. King wrote:
On 9/27/2011 10:47 AM, Bruno Marchal wrote:
On 27 Sep 2011, at 13:49, Stephen P. King wrote:
On 9/26/2011 7:56 PM, Jason Resch wrote:
<snip>
For well-defined propositions regarding the numbers I think the values are confined to true or false.
Jason
--
[SPK]
Not in general, unless one is only going to allow only Boolean logics to exist. There have been proven to exist logics that have truth values that range over any set of numbers, not just {0,1}. Recall the requirement for a mathematical structure to exist: Self-consistency.
Consistency is a notion applied usually to theories, or (chatty) machines, not to mathematical structures.
A theory is consistent if it does not prove some proposition and its negation. A machine is consistent if it does not assert a proposition and its negation.
[SPK]
Is not a machine represented mathematically by some abstract (mathematical ) structure? I am attempting to find clarity in the ideas surrounding the notion of "machine" and how you arrive at the idea that the abstract notion of implementation is sufficient to derive the physical notion of implementation.
This follows from the UD Argument, in the digital mechanist theory. No need of AUDA or complex math to understand the necessity of this, once we accept that we can survive with (physical, material) digital machines.
[SPK]
Is the property of universality independent of whether or not a machine has a set of properties? What is it that determines the properties of a machine? I need to understand better your definition of the word "machine".
In first order logic we have Gödel-Henkin completeness theorem which shows that a theory is consistent if and only if there is a mathematical structure (called model) satisfying (in a sense which can be made precise) the proposition proved in the theory.
[SPK]
What constraints are defined on the models by the Gödel-Henkin completeness theorem? How do we separate out effective consistent first-order theories that do not have computable models?
What do you mean by computable models?
[SPK]
Allow me to quote several definitions: "computable functions are exactly the functions that can be calculated using a mechanical calculation device given unlimited amounts of time and storage space. " (from http://en.wikipedia.org/wiki/Computable_function). "a computable model is one whose underlying set is decidable and whose functions and relations are uniformly computable. " (from http://arxiv.org/abs/math/0602483).
A computable model, as I understand it, could be considered as a representation of a system or structure whose properties can be determined by some process that can itself be represented as a function from the set of countable numbers to itself. This defintion seeks to abstractly represent the way that we can determine the properties of a physical system X or, equivalently, generate a finite list of operations that will create an instance of X.
[SPK]
Also, it is true that classical (Boolean) logic are not the only logic. There are infinitely many logics, below and above classical propositional logic. But this cannot be used to criticize the use of classical logic in some domain.
OK. My thought here was to show that classical (Boolean) logic is not unique and should not be taken as absolute. To do so would be a mistake similar to Kant's claim that Euclidean logic was absolute.
OK, but then why to use that fact to criticize Jason's defense of arithmetical truth independent of humans.
[SPK]
I am claiming a distinction between the existence of a structure and the definiteness of its properties.
It is my claim that prior to the establishment of whether or not a method of determining or deciding what the properties of a structure or system are, one can only consider the possibility of the structure or system. For example, say some proposition or sentence of a language exists. Does that existence determine the particulars of that proposition or sentence?
If it can how so? How do can we claim to be able to decide that P_i is true in the absence of a means to determine or decide what P_i means?
How do you know the meaning of these word "Unicorn"? Is the meaning of the word "Unicorn" something that that arises simply from the existence of sequence of symbols? is not meaning not something like a map between some set of properties instantiated entity and some set of instances of those properties in other entities? Consider an entity X that had a set of properties x_i that could not be related to those of any other entity? Would this prevent the existence of X?
The existence of X is the necessary possibility of X, []<>X.
All treatises on any non classical logic used classical (or much more rarely intuitionistic) logic at the meta-level. You will not find a book on fuzzy logic having fuzzy theorems, for example. Non classical logics have multiple use, which are not related with the kind of ontic truth we are looking for when searching a TOE.
[SPK]
Of course fuzzy logic does not have fuzzy theorem, that could be mistaking the meaning of the word "fuzzy" with the meaning of the word "ambiguous". I have been trying to establish the validity of the idea that it is the rules (given as axioms, etc) that are used to define a given mathematical structure, be it a model, or an algebra, etc. But I think that one must be careful that the logical structure that one uses of a means to define ontic truths is not assumed to be absolute unless very strong reasons can be proven to exist for such assumptions.
Usually non classical logic have epistemic or pragmatic classical interpretations, or even classical formulation, like the classical modal logic S4 which can emulate intuitionistic logic, or the Brouwersche modal logic B, which can emulate weak quantum logic. This corresponds to the fact that intuitionist logic might modelize constructive provability, and quantum logic modelizes observability, and not the usual notion of classical truth (as used almost everywhere in mathematics).
[SPK]
I use the orthocomplete lattices as a representation of quantum logic. My ideas are influenced by the work of Svozil, Calude and von Benthem, and others on this. I am not sure of the definition of "weak quantum logic" as you use it here.
Svozil, Calude and van Benthem thought on the subject are very good. Weak quantum logic is the logic of sublattice of ortholattices, like in the paper of Goldblatt that I have often refer to you. Basically it is quantum logic without the orthomodularity axiom. It does not distinguish finite dimensional pre-Hilbert space from Hilbert space, for example.
[SPK]
This paper http://www.jstor.org/pss/2274172 ? It seems to me that the distributivity axiom would not make the same distinction either, although Hilbert space is defined in terms of a linear algebra on a vector space. Consider this paper's abstract.
http://www.google.com/url?sa=t&rct=j&q=orthomodularity%20axiom&source=web&cd=5&sqi=2&ved=0CDgQFjAE&url=http%3A%2F%2Fm3k.grad.hr%2Fpapers-ps-pdf%2Fquantum-logic%2F1998-helv-phys-acta.pdf&ei=N3SETo2yFYGztwfLiYU0&usg=AFQjCNHal3UDb6B-MATSt1hloWFhSNVCnw&sig2=Fl7ESJLpFZ9qj8c8YU8S-w&cad=rja
"We show that binary orthologic becomes either quantum or classical logic when nothing but modus
ponens rule is added to it, depending on the kind of the operation of implication used. We also show that
in the usual approach the rule characterizes neither quantum nor classical logic. The diff erence turns out
to stem from the chosen valuation on a model of a logic. Thus algebraic mappings of axioms of standard
quantum logics would fail to yield an orthomodular lattice if a unary - as opposed to binary - valuation
were used. Instead, non-orthomodular nontrivial varieties of orthologic are obtained. We also discuss the
computational efficiency of the binary quantum logic and stress its importance for quantum computation
and related algorithms."
How can we even consider the distinction of one form of abstract structure, such as logical algebras or lattices, from another without there existing a means to generate instantiations of the two? This question goes to the heart of my skepticism of your result.
[SPK]
One question regarding the emulations. If one where considering only finite emulations of a quantum logic (such as how a classical approximation of a QM system could be considered), how might one apply the Tychonoff, Heine–Borel definition or Bolzano–Weierstrass criterion of compactness to be sure that compactness obtain for the models? If we use these compactness criteria, is it necessary that the collection of open sets that is used in complete in an absolute sense? Could it be that we have a way to recover the appearence of the axiom of choice or the ultrafilter lemma?
Hard and premature questions.
But do we not decide whether or not to pursue a conjecture by the implications of the conjecture? The questions that I am asking here are questions of the ability of the idea to give us an explanatory narrative that we can use to reason about our world. You are, with your result, proposing a result that implies an ontological theory: that Reality is, at its primitive level, purely abstract. This seems to be more of an echo of the ideas of Pythagoras than those of Plato...
Could it be possible to have a notion of accessibility to parametrize or weaking the word "every" as in the sentence: " A point x in X is a limit point of S if every open set containing x contains at least one point of S different from x itself." to "A point x in X is a limit point of S if every open set , that is assessible from some S, containing x contains at least one point of S different from x itself. The idea is that S and x cannot be an infinite distance (or infinite disjoint sequence of open sets) apart.
It seems to me that this would limit the implied omniscience of the compactness criteria (via the usual axiom of choice) and it seems more consistent with the notion that an emulation does not need to be *exact* to be informative.
Perhaps. Cerrtainly open problem in comp+Theaetetus.
[SPK]
Does that not imply that the explanatory value of comp+Theaetus is partly dependent of the resolution of such a problem? If we are going to seriously consider your form of ideal monism to be correct, as opposed to some form of non-substance dualism or material monism or neutral monism, do such questions not need to be looked at with seriousness? I am very interested in ontological theories, thus my queries.
[SPK]
To invoke the existence of non classical logic to throw a doubt about the universal truth of elementary statements in well defined domain, like arithmetic, would lead to complete relativism, given that you can always build some ad hoc logic/theory proving the negation of any statement, and this would make the notion of truth problematic. The contrary is true.
Relativism of that kind would be that last conclusion that I would desire! OTOH, we do need a clear notion of contextuality as illustrated by the way that words are defined in relation to other words in a dictionary.
I am problem driven. I start from the problem, and use the available math.
[SPK]
As am I. ;-) But I think that sometimes we need to look beyond the math and consider how it is that knowledge itself is possible.
A non classical logic is eventually accepted when we can find an interpretation of it in the classical framework.{SPK]
This seems to be an unnecessary prejudice! Why is the classical framework presumed to be the absolute measure of acceptability and, by implication, Reality?
No. Simplicity. Together with the need of the classical Church thesis, and our intuition of numbers. We do use the comp hypothesis, and it needs classical logic on the natural numbers. Intuitionist logic can also be used, but then the math are much more complex, and eventually we need a non trivial use of the double negation topology. It is more easy to use, like usually in math, the meta-classical background.
[SPK]
But it seems that you are assuming that our ability to have intuitions of abstractions itself has a satisfactory explanation.
You seem to assume that the properties of, for example, memory obtain solely from the existence of Arithmetic and that such existence is severable from the physical instantiations of memory.
This statement seems to reveal an explanation of why you believe that QM is derivative of classical logic somehow in spite of my repeated statements to the work of others that show that this is simply not possible except in a crude and non-faithful manner!
You repeatedly confuse the notion of embedding of a logic in another, and representing a logic in another. I have explained this many times, but you keep coming back on that confusion. QL cannot be faithfully extended in Boolean logic, but this does not mean that you cannot represent QL in a classical frame work (like it is done all the time; quantum mechanics is itself a classical theory).
[SPK]
How is a representation of logic A in logic B not equivalent to an embedding of A in B? Maybe I am conflating a model with a representation.
[SPK]
A non standard truth set, like the collection of open subsets of a topological space, provided a classical sense for intuitionist logic, like a lattice of linear subspaces can provide a classical interpretation of quantum logic (indeed quantum logic is born from such structures). It might be that nature observables obeys quantum logic, but quantum physicists talk and reason in classical logic, and use classical mathematical tools to describe the non classical behavior of matter.
I agree but will point out that the use of classical logic could be merely a habit and convenience.
Classical logic allows non constructive reasoning which are obligatory in any modest theology, like the machine's theologies.Do you agree that a (mathematical) machine stop or ... do not stop, on some input. We don't need more than that.
[SPK]
A mathematical object, as I can understand it, is purely an abstraction that supervenes upon the actions of a mind to have a meaning. The particular properties of the object flow from the rules, axioms, etc. that are used to define said object and do not depend on anything else except the possibility of some instantiation of those rules, axioms, etc.
If a "machine" is a form of mathematical structure
then its existence is not predicated on any particular instantiation of such a machine but its properties are not defined by the mere possibility of its existence. Additionally, the notion of "stopping" or "not stopping" has a meaning that refers to a process in some way. A process cannot be reduced to a static relation between abstract entities but it can be represented by sequences of static relations. I distinguish between the representation of a process and the process itself. A map is not the territory.
OTOH, if we consider the idea that we can relate simulations of a given process with the process itself, we are comparing one form of process to another, not a static set of relations to a process. I do not think of mathematical objects as static relations only, I see them more as invariant patterns that occur in a background of eternal interactions between possible aspects of Existence.
[SPK]
I think that there may be a reason why classical logics are taken as fundamental, but this reasoning is build on the intuition that a 3p "public" notion of communication can only be defined in Boolean logical terms; in other words, we observe a classical reality because that is the manner that maximally consistent collections of open sets can bisimulate each other. Bisimulation is communication between and within logical systems. If bisimulation cannot occur between a pair of logics then there is no interactions between the topological spaces dual to those logics. This gives us a way to think of seperate physical worlds. But this reasoning requires that we treat logics and topological spaces on an equal ontological footing. Logic cannot be taken as the unique ontological aspect of existence.
It follows from the step 8 of UDA that if we are machine, classical arithmetic is a theory of everything. Non classical logics are recovered in the machine's epistemologies. S4grz1 is intuitionist and the Z1* and X1* logics are type of quantum logics.
If we are some abstract static relational structure then Arithmetic is an explanation of everything?
Maybe for an abstract and static entity, but not for an entity that needs to explain the appearance of a universe that is never only identically itself. I do not identify an arbitrary collection of static relations with Change in a decidable one to one and onto way.
Bruno Marchal
The ineffable is so much ineffable that even just writing one sentence
on it can only completely miss the point.
In fact, your very question answers it: we are near a diagonal self-
defeating sentence. Those are the fixed point of p <---> ~Bp, and are
of type Dt. So they belong to G* minus G. They obey the laws Bx --> ~x.
And so, if I was a wise guy, I should either shut my mouth, or explain
that "If moral makes sense, then we can't communicate that moral", or
something like that.
Moral is a bet in a better reality, and thus Dt, by completeness, for
Löbian entity talking firs order logic. (~Bf <-> there is a model/
reality). That is another path for justifying that link.
Lao Tseu, Plotinus, etc. All the mystic, capable if being a bit
rationalist knows that they should better NOT talk. That is why the
ideal machine keeps so much silence on the deep question. Thanks to
G*, many no provable proposition (rationally communicable,
justifiable) can be justified by assuming some reflexion principle,
like Dt (Bf -> f), or stronger.
But it is here that the LUMs can easily fall in the pseudo-theological
trap.
Bruno
PS This comes more from AUDA, than UDA. But UDA is enough to explain
that "if we are moral enough then we cannot enforce anyone in
believing that he will survive, or just be satisfied, with an
artificial brain (or even an aspirin). The truth of comp, or aspirin
(btw), is in personal judgement, evaluation and possible (risky)
experiences. That's number life!
Stephen P. King
On 29 Sep 2011, at 16:36, Stephen P. King wrote:
On 9/29/2011 4:03 AM, Bruno Marchal wrote:
On 28 Sep 2011, at 16:44, Stephen P. King wrote:
On 9/27/2011 10:47 AM, Bruno Marchal wrote:
On 27 Sep 2011, at 13:49, Stephen P. King wrote:
On 9/26/2011 7:56 PM, Jason Resch wrote:
<snip>
For well-defined propositions regarding the numbers I think the values are confined to true or false.
Jason
--�[SPK]
��� Not in general, unless one is only going to allow only Boolean logics to exist. There have been proven to exist logics that have truth values that range over any set of numbers, not just {0,1}. Recall the requirement for a mathematical structure to exist: Self-consistency.
Consistency is a notion applied usually to theories, or (chatty) machines, not to mathematical structures.
A theory is consistent if it does not prove some proposition and its negation. A machine is consistent if it does not assert a proposition and its negation.
[SPK]
��� Is not a machine represented mathematically by some abstract (mathematical ) structure?� I am attempting to find clarity in the ideas surrounding the notion of "machine" and how you arrive at the idea that the abstract notion of implementation is sufficient to derive the physical notion of implementation.
This follows from the UD Argument, in the digital mechanist theory. No need of AUDA or complex math to understand the necessity of this, once we accept that we can survive with (physical, material) digital machines.
[SPK]
��� Is the property of universality independent of whether or not a machine has a set of properties? What is it that determines the properties of a machine? I need to understand better your definition of the word "machine".
It is anything that can be emulated by a universal turing machines. With Church thesis, I don't have to be much more precise than that. Once you have one universal system, it emulates all possible machines, and the UD emulates them all effectively.So in any physical universe emulating a UD, we are already there, and physics has to be retrieved from some statistics on the computations.And the movie graph argument explained that the "natural" emulation of a UD made by the natural numbers through their additive and multiplicative relations is enough.
In first order logic we have G�del-Henkin completeness theorem which shows that a theory is consistent if and only if there is a mathematical structure (called model) satisfying (in a sense which can be made precise) the proposition proved in the theory.
[SPK]
��� What constraints are defined on the models by the G�del-Henkin completeness theorem? How do we separate out effective consistent first-order theories that do not have computable models?
What do you mean by computable models?
[SPK]
��� Allow me to quote several definitions: "computable functions are exactly the functions that can be calculated using a mechanical calculation device given unlimited amounts of time and storage space. " (from http://en.wikipedia.org/wiki/Computable_function).� "a computable model is one whose underlying set is decidable and whose functions and relations are uniformly computable. " (from http://arxiv.org/abs/math/0602483).
Which functions and relations? Those corresponding to the primitive terms of the theory, or all relations?If it is the first case, then this would give the standard model (in case the theory is first order arithmetic).
[SPK]I am not sure I see your point.�
��� Could you have communicated this question to me if it was impossible to create a physical instance of the question? How to minds interact? I say that they interact via bisimulation and, dually, by topological transformations between Stone-type spaces.
��� A computable model, as I understand it, could be considered as a representation of a system or structure whose properties can be determined by some process that can itself be represented as a function from the set of countable numbers to itself. This defintion seeks to abstractly represent the way that we can determine the properties of a physical system X or, equivalently, generate a finite list of operations that will create an instance of X.
?
[SPK]
Also, it is true that classical (Boolean) logic are not the only logic. There are infinitely many logics, below and above classical propositional logic. But this cannot be used to criticize the use of classical logic in some domain.
��� OK. My thought here was to show that classical (Boolean) logic is not unique and should not be taken as absolute. To do so would be a mistake similar to Kant's claim that Euclidean logic was absolute.
OK, but then why to use that fact to criticize Jason's defense of arithmetical truth independent of humans.
[SPK][SPK]
��� I am claiming a distinction between the existence of a structure and the definiteness of its properties.
I limit existence to natural numbers. The rest is numbers imagination to try to understand the numbers. "existence of a structure" has some sense in some mathematical theories, which I can believe genuine and even useful for the epistemology of numbers, but I am neutral on the nature of that existence, beyond belonging to the internal mindscape of the machine (which is really already beyond mathematics.�
��� Some people might think that this a bigotry of the worst kind. To imagine that all that exists in limited by what a particular kind of finite entity can count, such a chauvinism! You forget that our method of counting is a by-product of our physics. As Deutsch explains, the physics that our universe of experience has is not unique. Different laws of physics generate differnt forms of possible counting and thus different concepts of numbers for entities existing in those universes.
It is my claim that prior to the establishment of whether or not a method of determining or deciding what the properties of a structure or system are, one can only consider the possibility of the structure or system. For example, say some proposition or sentence of a language exists. Does that existence determine the particulars of that proposition or sentence?
That is very unclear.
��� Does the mere existence of an unspecified sentence determine its possible meanings?
If it can how so? How do can we claim to be able to decide that P_i is true in the absence of a means to determine or decide what P_i means?
It can be true even if we can't decide it is. This makes sense for the arithmetical relations (but indeed it is far more complex for sets, and machine epistemology).It seems clear to me that one of the following two sentences is true, and the other one false:There is an infinity of twin primes.There is a biggest twin prime.OK?If you are OK, then you agree, by definition, with the minimal (arithmetical) realism we need to give sense to mechanism.
��� Not OK. If you (or any one that you could instruct) where unable to write those sentences, what meaning would they have? How can we ignore the fact that symbolic, iconic or whatever form of representations, with which we communicate ideas, cannot occur absent a physical world with some definite physical laws. This does not mean that such as ontologically primitive, not at all. It means that one must give equal ontological weight to the appearances of physical worlds in the 1p as we give to the abstract mathematical entities that they are implementing. I invite you to read Bertrand Russell's article on neutral monism
http://cco.cambridge.org/extract?id=ccol0521631785_CCOL0521631785A012.� He has a much better command of the explanation of this idea than I do. I am just a curious student studying my books and asking questions.
��� How do you know the meaning of these word "Unicorn"? Is the meaning of the word "Unicorn" something that that arises simply from the existence of sequence of symbols? is not meaning not something like a map between some set of properties instantiated entity and some set of instances of those properties in other entities? Consider an entity X that had a set of properties x_i that could not be related to those of any other entity? Would this prevent the existence of X?
The existence of X is the necessary possibility of X, []<>X.
I like that. As you know X ->[]<>X (which i write �p ->�[]<>X) is the initial abstract equation of physics already gathered by the interview with the LUM. here X is a sigma_1 sentence, and []x means Bx & Dt, with B = G�del's beweisbar (and <> = ~[]~, and D = ~B~, as usual).
Does a unicorn exists. I don't know, and I am not sure "unicorn" is well defined, nor "exist" in this case. Same for the moon, to be sure.
[SPK]
��� Surely it can exist, but what properties does it have? We simply do not know.
All treatises on any non classical logic used classical (or much more rarely intuitionistic) logic at the meta-level. You will not find a book on fuzzy logic having fuzzy theorems, for example. Non classical logics have multiple use, which are not related with the kind of ontic truth we are looking for when searching a TOE.
[SPK]
��� Of course fuzzy logic does not have fuzzy theorem, that could be mistaking the meaning of the word "fuzzy" with the meaning of the word "ambiguous". I have been trying to establish the validity of the idea that it is the rules (given as axioms, etc) that are used to define a given mathematical structure, be it a model, or an algebra, etc. But I think that one must be careful that the logical structure that one uses of a means to define ontic truths is not assumed to be absolute unless very strong reasons can be proven to exist for such assumptions.
Usually non classical logic have epistemic or pragmatic classical interpretations, or even classical formulation, like the classical modal logic S4 which can emulate intuitionistic logic, or the Brouwersche modal logic B, which can emulate weak quantum logic. This corresponds to the fact that intuitionist logic might modelize constructive provability, and quantum logic modelizes observability, and not the usual notion of classical truth (as used almost everywhere in mathematics).
[SPK]
��� I use the orthocomplete lattices as a representation of quantum logic. My ideas are influenced by the work of Svozil, Calude� and von Benthem, and others on this. I am not sure of the definition of "weak quantum logic" as you use it here.
Svozil, Calude and van Benthem thought on the subject are very good. Weak quantum logic is the logic of sublattice of ortholattices, like in the paper of Goldblatt that I have often refer to you. Basically it is quantum logic without the orthomodularity axiom. It does not distinguish finite dimensional pre-Hilbert space from Hilbert space, for example.
[SPK]
��� This paper http://www.jstor.org/pss/2274172 ? It seems to me that the distributivity axiom would not make the same distinction either, although Hilbert space is defined in terms of a linear algebra on a vector space. Consider this paper's abstract.
http://www.google.com/url?sa=t&rct=j&q=orthomodularity%20axiom&source=web&cd=5&sqi=2&ved=0CDgQFjAE&url=http%3A%2F%2Fm3k.grad.hr%2Fpapers-ps-pdf%2Fquantum-logic%2F1998-helv-phys-acta.pdf&ei=N3SETo2yFYGztwfLiYU0&usg=AFQjCNHal3UDb6B-MATSt1hloWFhSNVCnw&sig2=Fl7ESJLpFZ9qj8c8YU8S-w&cad=rja
"We show that binary orthologic becomes either quantum or classical logic when nothing but modus
ponens rule is added to it, depending on the kind of the operation of implication used. We also show that
in the usual approach the rule characterizes neither quantum nor classical logic. The diff erence turns out
to stem from the chosen valuation on a model of a logic. Thus algebraic mappings of axioms of standard
quantum logics would fail to yield an orthomodular lattice if a unary - as opposed to binary - valuation
were used. Instead, non-orthomodular nontrivial varieties of orthologic are obtained. We also discuss the
computational efficiency of the binary quantum logic and stress its importance for quantum computation
and related algorithms."
[SPK]��� How can we even consider the distinction of one form of abstract structure, such as logical algebras or lattices, from another without there existing a means to generate instantiations of the two? This question goes to the heart of my skepticism of your result.
I don't see any relation between the quote, and your comment.�And what do you mean by instantiation? Do you mean physical instantiation, or mathematical instantiation. From inside, UDA shows that universal machine (even physically instantiated one, even assuming primitive matter) cannot distinguish them.�
��� OK, but do you not see that this result might explain the conflation of physical and mathematical notions of implementation if one is thinking only according to UDA? I see them as different because I do not think in symbolic forms. It is a disability of� sequential brain processing and memory (dyslexia) that prevents my delusion. How ironic.
My result is: mechanism entails immateralism (matter can exist but as no more any relation with consciousness, and so is eliminated with the usual weak occam principle). This should be a problem for you if you want to keep both mechanism and weak materialism, but why do you want to do that. On the contrary, mechanism makes the laws of physics much more solid and stable, by providing an explanation relying only on diophantine addition and multiplication.
��� I reject all form of monism except neutral monism. Existence itself is the only primitive.
[SPK]
[SPK]
��� One question regarding the emulations. If one where considering only finite emulations of a quantum logic (such as how a classical approximation of a QM system could be considered), how might one apply the Tychonoff, Heine�Borel definition or Bolzano�Weierstrass criterion of compactness to be sure that compactness obtain for the models? If we use these compactness criteria, is it necessary that the collection of open sets that is used in complete in an absolute sense? Could it be that we have a way to recover the appearence of the axiom of choice or the ultrafilter lemma?
Hard and premature questions.
��� But do we not decide whether or not to pursue a conjecture by the implications of the conjecture? The questions that I am asking here are questions of the ability of the idea to give us an explanatory narrative that we can use to reason about our world. You are, with your result, proposing a result that implies an ontological theory: that Reality is, at its primitive level, purely abstract. This seems to be more of an echo of the ideas of Pythagoras than those of Plato...
Sure! �Like the neoplatonist, the UMs seems to have a pythagorean ontology. An annex of my french thesis has the title: "Church Thesis rehabilitate Pythagorism".
��� :-)
��� Could it be possible to have a notion of accessibility to parametrize or weaking the word "every" as in the sentence: " A point x in X is a limit point of S if every open set containing x contains at least one point of S different from x itself." to "A point x in X is a limit point of S if every open set , that is assessible from some S, containing x contains at least one point of S different from x itself. The idea is that S and x cannot be an infinite distance (or infinite disjoint sequence of open sets) apart.
��� It seems to me that this would limit the implied omniscience of the compactness criteria (via the usual axiom of choice) and it seems more consistent with the notion that an emulation does not need to be *exact* to be informative.
Perhaps. Cerrtainly open problem in comp+Theaetetus.
[SPK]
��� Does that not imply that the explanatory value of comp+Theaetus is partly dependent of the resolution of such a problem? If we are going to seriously consider your form of ideal monism to be correct, as opposed to some form of non-substance dualism or material monism or neutral monism, do such questions not need to be looked at with seriousness? I am very interested in ontological theories, thus my queries.
Comp gives neutral monism. It is ideal is you want the numbers to be idea, but then they are idea of God. But that move is not strictly necessary.
I don't defend mechanism, Stephen. I am a logician, I just show that mechanism and weak materialism does not work together, and I show the consistence of mechanism, by showing that the UMs can understand this already.
[SPK]
��� And I agree with your result, it follows unassailably from its premises. I am just trying to get you to see that there is more that you seem to not wish to see.
�
[SPK]
To invoke the existence of non classical logic to throw a doubt about the universal truth of elementary statements in well defined domain, like arithmetic, would lead to complete relativism, given that you can always build some ad hoc logic/theory proving the negation of any statement, and this would make the notion of� truth problematic. The contrary is true.
��� Relativism of that kind would be that last conclusion that I would desire! OTOH, we do need a clear notion of contextuality as illustrated by the way that words are defined in relation to other words in a dictionary.
I am problem driven. I start from the problem, and use the available math.
[SPK]
��� As am I. ;-) But I think that sometimes we need to look beyond the math and consider how it is that knowledge itself is possible.
Yeah, sure. That is the main object of the whole work, and Theaetetus, and all the hypostases. "Beyond the math" is done before the math, because the UDA is not in math at all. It is at the cross of cognitive and matter science. Then the UDA explains entirely why arithmetic (or combinators, ...) plays some fundamental role.
[SPK]
��� Might the UD itself have a topological dual? Is it sequentially compact?
A non classical logic is eventually accepted when we can find an interpretation of it in the classical framework.{SPK]
��� This seems to be an unnecessary prejudice! Why is the classical framework presumed to be the absolute measure of acceptability and, by implication, Reality?
No. Simplicity. Together with the need of the classical Church thesis, and our intuition of numbers. We do use the comp hypothesis, and it needs classical logic on the natural numbers. Intuitionist logic can also be used, but then the math are much more complex, and eventually we need a non trivial use of the double negation topology. It is more easy to use, like usually in math, the meta-classical background.�
[SPK]
��� But it seems that you are assuming that our ability to have intuitions of abstractions itself has a satisfactory explanation.
I don't address that question, except with the mathematical self-reference a shadow of solution appears, perhaps.
[SPK]
��� Any hints that I might study?
You seem to assume that the properties of, for example, memory obtain solely from the existence of Arithmetic and that such existence is severable from the physical instantiations of memory.
I don't assume that at all. It is the result! You have to study it. It is much simpler than you seem to think.�
My only assumption is that the brain works like a machine, + CT to give sense to the word machine, and to relate.�
That memory exists in arithmetic is obvious, once you understand that arithmetic emulate all computations. That physical memories arise is more subtle to show, but that is the point of the whole UDA.
[SPK]
��� /shakes head ... Sometimes I wonder if you are choosing not to see past your formulas. :-(
This statement seems to reveal an explanation of why you believe that QM is derivative of classical logic somehow in spite of my repeated statements to the work of others that show that this is simply not possible except in a crude and non-faithful manner!
You repeatedly confuse the notion of embedding of a logic in another, and representing a logic in another. I have explained this many times, but you keep coming back on that confusion. QL cannot be faithfully extended in Boolean logic, but this does not mean that you cannot represent QL in a classical frame work (like it is done all the time; quantum mechanics is itself a classical theory).
[SPK]
��� How is a representation of logic A in logic B not equivalent to an embedding of A in B? Maybe I am conflating a model with a representation.
For an embedding you need some injective morphism. For a representation you need a mean to translate the theorems.
QL is not embeddable in classical logic (it means, roughly that you cannot have hidden variable), but QL can be interpreted by many classical structures (lattice, modal B systems, etc.).�
[SPK]
��� Thank you for this definition. I have been unable to find it in the literature so far.
[SPK]
A non standard truth set, like the collection of open subsets of a topological space, provided a classical sense for intuitionist logic, like a lattice of linear subspaces can provide a classical interpretation of quantum logic (indeed quantum logic is born from such structures). It might be that nature observables obeys quantum logic, but quantum physicists talk and reason in classical logic, and use classical mathematical tools to describe the non classical behavior of matter.
��� I agree but will point out that the use of classical logic could be merely a habit and convenience.
Classical logic allows non constructive reasoning which are obligatory in any modest theology, like the machine's theologies.Do you agree that a (mathematical) machine stop or ... do not stop, on some input. We don't need more than that.
[SPK]
��� A mathematical object, as I can understand it, is purely an abstraction that supervenes upon the actions of a mind to have a meaning. The particular properties of the object flow from the rules, axioms, etc. that are used to define said object and do not depend on anything else except the possibility of some instantiation of those rules, axioms, etc.
In logic, the model are the intantiations, but they are mathematical structure.
[SPK]
��� Might you read pages 187-193 of David Deutsch's new book, The Beginning of Infinity. He elaborates the problem that I see with this claim that you are making. I just found the argument in Deutsch's book last week and was very surprised that it is not "common sense".
If a "machine" is a form of mathematical structure
Better to see a machine as a relative number. It might be wriiten in sophisticated language, like quantum topology, giving them complex shape, but they are still relative numbers. This follows from the digital condition, which is assume for the machine we talk about in the comp framework.
��� OK.
then its existence is not predicated on any particular instantiation of such a machine but its properties are not defined by the mere possibility of its existence. Additionally, the notion of "stopping" or "not stopping" has a meaning that refers to a process in some way. A process cannot be reduced to a static relation between abstract entities but it can be represented by sequences of static relations. I distinguish between the representation of a process and the process itself. A map is not the territory.
Arithmetical truth is the territory. Machines and numbers are what build maps of the territory. When you say "yes" to a doctor, you are just changing a map for another. Nowhere is a confusion between map and territory, except for the fixed points, like the here and now indexical consciousness. But we can be thankful that this is possible (in computer science) because it makes the map/brain useful when relating with a probable part of the territory.
[SPK]
��� But are when maps and territories are made of the "same stuff" we have problems.
��� OTOH, if we consider the idea that we can relate simulations of a given process with the process itself, we are comparing one form of process to another, not a static set of relations to a process. I do not think of mathematical objects as static relations only, I see them more as invariant patterns that occur in a background of eternal interactions between possible aspects of Existence.
The question was: do you agree that phi_i(j) always either gives a result, or does not give a result.
[SPK]
��� If phi_i(j) can be instantiated by a topological space, yes. No, if it cannot be.
[SPK]
I think that there may be a reason why classical logics are taken as fundamental, but this reasoning is build on the intuition that a 3p "public" notion of communication can only be defined in Boolean logical terms; in other words, we observe a classical reality because that is the manner that maximally consistent collections of open sets can bisimulate each other. Bisimulation is communication between and within logical systems. If bisimulation cannot occur between a pair of logics then there is no interactions between the topological spaces dual to those logics. This gives us a way to think of seperate physical worlds. But this reasoning requires that we treat logics and topological spaces on an equal ontological footing. Logic cannot be taken as the unique ontological aspect of existence.
It follows from the step 8 of UDA that if we are machine, classical arithmetic is a theory of everything. Non classical logics are recovered in the machine's epistemologies. S4grz1 is intuitionist and the Z1* and X1* logics are type of quantum logics.
��� If we are some abstract static relational structure then Arithmetic is an explanation of everything?
No. If we are digital machine (physical, material, or not) then physics has to be explained by statistics on computations, viewed from an angle.
It is not an explanation at all. It is a consequence of having a brain functioning by obeying laws (UDA).
AUDA seems to illustrate that this is quite possible, given that it shows that the measure one on the computation, if it exist, give rise to a quantum like physics.
[SPK]
��� That remains to be proven. We must show how a measure obtains for this result.
Maybe for an abstract and static entity, but not for an entity that needs to explain the appearance of a universe that is never only identically itself. I do not identify an arbitrary collection of static relations with Change in a decidable one to one and onto way.
Just say no to the doctor then. This means you take physical time as a primitive again, and UDA shows that this does not work if we can survive from a material brain transplant. Besides I am not sure that Change has physical sense with current physics too, nor even what you mean by that. Prigogine also believed in a basic primitive time, but he did not convince me on this.
Bruno
��� I tend to not trust anyone, especially "experts". My ideas about time where molded by the reasoning of Hitoshi Kitada et al. You might read his papers some day.
Onward!
Stephen
Bruno Marchal
On 9/29/2011 2:15 PM, Bruno Marchal wrote:
On 29 Sep 2011, at 16:36, Stephen P. King wrote:
On 9/29/2011 4:03 AM, Bruno Marchal wrote:
On 28 Sep 2011, at 16:44, Stephen P. King wrote:
On 9/27/2011 10:47 AM, Bruno Marchal wrote:
On 27 Sep 2011, at 13:49, Stephen P. King wrote:
On 9/26/2011 7:56 PM, Jason Resch wrote:
<snip>
For well-defined propositions regarding the numbers I think the values are confined to true or false.
Jason
--
[SPK]
Not in general, unless one is only going to allow only Boolean logics to exist. There have been proven to exist logics that have truth values that range over any set of numbers, not just {0,1}. Recall the requirement for a mathematical structure to exist: Self-consistency.
Consistency is a notion applied usually to theories, or (chatty) machines, not to mathematical structures.
A theory is consistent if it does not prove some proposition and its negation. A machine is consistent if it does not assert a proposition and its negation.
[SPK]
Is not a machine represented mathematically by some abstract (mathematical ) structure? I am attempting to find clarity in the ideas surrounding the notion of "machine" and how you arrive at the idea that the abstract notion of implementation is sufficient to derive the physical notion of implementation.
This follows from the UD Argument, in the digital mechanist theory. No need of AUDA or complex math to understand the necessity of this, once we accept that we can survive with (physical, material) digital machines.
[SPK]
Is the property of universality independent of whether or not a machine has a set of properties? What is it that determines the properties of a machine? I need to understand better your definition of the word "machine".
It is anything that can be emulated by a universal turing machines. With Church thesis, I don't have to be much more precise than that. Once you have one universal system, it emulates all possible machines, and the UD emulates them all effectively.So in any physical universe emulating a UD, we are already there, and physics has to be retrieved from some statistics on the computations.And the movie graph argument explained that the "natural" emulation of a UD made by the natural numbers through their additive and multiplicative relations is enough.
In first order logic we have Gödel-Henkin completeness theorem which shows that a theory is consistent if and only if there is a mathematical structure (called model) satisfying (in a sense which can be made precise) the proposition proved in the theory.
[SPK]
What constraints are defined on the models by the Gödel-Henkin completeness theorem? How do we separate out effective consistent first-order theories that do not have computable models?
What do you mean by computable models?
[SPK]
Allow me to quote several definitions: "computable functions are exactly the functions that can be calculated using a mechanical calculation device given unlimited amounts of time and storage space. " (from http://en.wikipedia.org/wiki/Computable_function). "a computable model is one whose underlying set is decidable and whose functions and relations are uniformly computable. " (from http://arxiv.org/abs/math/0602483).
Which functions and relations? Those corresponding to the primitive terms of the theory, or all relations?If it is the first case, then this would give the standard model (in case the theory is first order arithmetic).I am not sure I see your point.
[SPK]
Could you have communicated this question to me if it was impossible to create a physical instance of the question?
How to minds interact?
I say that they interact via bisimulation and, dually, by topological transformations between Stone-type spaces.
A computable model, as I understand it, could be considered as a representation of a system or structure whose properties can be determined by some process that can itself be represented as a function from the set of countable numbers to itself. This defintion seeks to abstractly represent the way that we can determine the properties of a physical system X or, equivalently, generate a finite list of operations that will create an instance of X.
?
[SPK]
Also, it is true that classical (Boolean) logic are not the only logic. There are infinitely many logics, below and above classical propositional logic. But this cannot be used to criticize the use of classical logic in some domain.
OK. My thought here was to show that classical (Boolean) logic is not unique and should not be taken as absolute. To do so would be a mistake similar to Kant's claim that Euclidean logic was absolute.
OK, but then why to use that fact to criticize Jason's defense of arithmetical truth independent of humans.
[SPK]
I am claiming a distinction between the existence of a structure and the definiteness of its properties.
I limit existence to natural numbers. The rest is numbers imagination to try to understand the numbers. "existence of a structure" has some sense in some mathematical theories, which I can believe genuine and even useful for the epistemology of numbers, but I am neutral on the nature of that existence, beyond belonging to the internal mindscape of the machine (which is really already beyond mathematics.
[SPK]
Some people might think that this a bigotry of the worst kind.
To imagine that all that exists in limited by what a particular kind of finite entity can count, such a chauvinism!
You forget that our method of counting is a by-product of our physics.
As Deutsch explains, the physics that our universe of experience has is not unique. Different laws of physics generate differnt forms of possible counting and thus different concepts of numbers for entities existing in those universes.
It is my claim that prior to the establishment of whether or not a method of determining or deciding what the properties of a structure or system are, one can only consider the possibility of the structure or system. For example, say some proposition or sentence of a language exists. Does that existence determine the particulars of that proposition or sentence?
That is very unclear.
[SPK]
Does the mere existence of an unspecified sentence determine its possible meanings?
[SPK]
If it can how so? How do can we claim to be able to decide that P_i is true in the absence of a means to determine or decide what P_i means?
It can be true even if we can't decide it is. This makes sense for the arithmetical relations (but indeed it is far more complex for sets, and machine epistemology).It seems clear to me that one of the following two sentences is true, and the other one false:There is an infinity of twin primes.There is a biggest twin prime.OK?If you are OK, then you agree, by definition, with the minimal (arithmetical) realism we need to give sense to mechanism.
Not OK. If you (or any one that you could instruct) where unable to write those sentences, what meaning would they have?
How can we ignore the fact that symbolic, iconic or whatever form of representations, with which we communicate ideas, cannot occur absent a physical world with some definite physical laws.
This does not mean that such as ontologically primitive, not at all. It means that one must give equal ontological weight to the appearances of physical worlds in the 1p as we give to the abstract mathematical entities that they are implementing.
I invite you to read Bertrand Russell's article on neutral monism
http://cco.cambridge.org/extract?id=ccol0521631785_CCOL0521631785A012. He has a much better command of the explanation of this idea than I do. I am just a curious student studying my books and asking questions.
How do you know the meaning of these word "Unicorn"? Is the meaning of the word "Unicorn" something that that arises simply from the existence of sequence of symbols? is not meaning not something like a map between some set of properties instantiated entity and some set of instances of those properties in other entities? Consider an entity X that had a set of properties x_i that could not be related to those of any other entity? Would this prevent the existence of X?
The existence of X is the necessary possibility of X, []<>X.
I like that. As you know X ->[]<>X (which i write p -> []<>X) is the initial abstract equation of physics already gathered by the interview with the LUM. here X is a sigma_1 sentence, and []x means Bx & Dt, with B = Gödel's beweisbar (and <> = ~[]~, and D = ~B~, as usual).
Does a unicorn exists. I don't know, and I am not sure "unicorn" is well defined, nor "exist" in this case. Same for the moon, to be sure.
[SPK]
Surely it can exist, but what properties does it have? We simply do not know.
All treatises on any non classical logic used classical (or much more rarely intuitionistic) logic at the meta-level. You will not find a book on fuzzy logic having fuzzy theorems, for example. Non classical logics have multiple use, which are not related with the kind of ontic truth we are looking for when searching a TOE.
[SPK]
Of course fuzzy logic does not have fuzzy theorem, that could be mistaking the meaning of the word "fuzzy" with the meaning of the word "ambiguous". I have been trying to establish the validity of the idea that it is the rules (given as axioms, etc) that are used to define a given mathematical structure, be it a model, or an algebra, etc. But I think that one must be careful that the logical structure that one uses of a means to define ontic truths is not assumed to be absolute unless very strong reasons can be proven to exist for such assumptions.
Usually non classical logic have epistemic or pragmatic classical interpretations, or even classical formulation, like the classical modal logic S4 which can emulate intuitionistic logic, or the Brouwersche modal logic B, which can emulate weak quantum logic. This corresponds to the fact that intuitionist logic might modelize constructive provability, and quantum logic modelizes observability, and not the usual notion of classical truth (as used almost everywhere in mathematics).
[SPK]
I use the orthocomplete lattices as a representation of quantum logic. My ideas are influenced by the work of Svozil, Calude and von Benthem, and others on this. I am not sure of the definition of "weak quantum logic" as you use it here.
Svozil, Calude and van Benthem thought on the subject are very good. Weak quantum logic is the logic of sublattice of ortholattices, like in the paper of Goldblatt that I have often refer to you. Basically it is quantum logic without the orthomodularity axiom. It does not distinguish finite dimensional pre-Hilbert space from Hilbert space, for example.
[SPK]
This paper http://www.jstor.org/pss/2274172 ? It seems to me that the distributivity axiom would not make the same distinction either, although Hilbert space is defined in terms of a linear algebra on a vector space. Consider this paper's abstract.
http://www.google.com/url?sa=t&rct=j&q=orthomodularity%20axiom&source=web&cd=5&sqi=2&ved=0CDgQFjAE&url=http%3A%2F%2Fm3k.grad.hr%2Fpapers-ps-pdf%2Fquantum-logic%2F1998-helv-phys-acta.pdf&ei=N3SETo2yFYGztwfLiYU0&usg=AFQjCNHal3UDb6B-MATSt1hloWFhSNVCnw&sig2=Fl7ESJLpFZ9qj8c8YU8S-w&cad=rja
"We show that binary orthologic becomes either quantum or classical logic when nothing but modus
ponens rule is added to it, depending on the kind of the operation of implication used. We also show that
in the usual approach the rule characterizes neither quantum nor classical logic. The diff erence turns out
to stem from the chosen valuation on a model of a logic. Thus algebraic mappings of axioms of standard
quantum logics would fail to yield an orthomodular lattice if a unary - as opposed to binary - valuation
were used. Instead, non-orthomodular nontrivial varieties of orthologic are obtained. We also discuss the
computational efficiency of the binary quantum logic and stress its importance for quantum computation
and related algorithms."
How can we even consider the distinction of one form of abstract structure, such as logical algebras or lattices, from another without there existing a means to generate instantiations of the two? This question goes to the heart of my skepticism of your result.
I don't see any relation between the quote, and your comment.
And what do you mean by instantiation? Do you mean physical instantiation, or mathematical instantiation. From inside, UDA shows that universal machine (even physically instantiated one, even assuming primitive matter) cannot distinguish them.
[SPK]
OK, but do you not see that this result might explain the conflation of physical and mathematical notions of implementation if one is thinking only according to UDA? I see them as different because I do not think in symbolic forms. It is a disability of sequential brain processing and memory (dyslexia) that prevents my delusion. How ironic.
My result is: mechanism entails immateralism (matter can exist but as no more any relation with consciousness, and so is eliminated with the usual weak occam principle). This should be a problem for you if you want to keep both mechanism and weak materialism, but why do you want to do that. On the contrary, mechanism makes the laws of physics much more solid and stable, by providing an explanation relying only on diophantine addition and multiplication.
[SPK]
I reject all form of monism except neutral monism. Existence itself is the only primitive.
[SPK]
One question regarding the emulations. If one where considering only finite emulations of a quantum logic (such as how a classical approximation of a QM system could be considered), how might one apply the Tychonoff, Heine–Borel definition or Bolzano–Weierstrass criterion of compactness to be sure that compactness obtain for the models? If we use these compactness criteria, is it necessary that the collection of open sets that is used in complete in an absolute sense? Could it be that we have a way to recover the appearence of the axiom of choice or the ultrafilter lemma?
Hard and premature questions.
But do we not decide whether or not to pursue a conjecture by the implications of the conjecture? The questions that I am asking here are questions of the ability of the idea to give us an explanatory narrative that we can use to reason about our world. You are, with your result, proposing a result that implies an ontological theory: that Reality is, at its primitive level, purely abstract. This seems to be more of an echo of the ideas of Pythagoras than those of Plato...
[SPK]
Sure! Like the neoplatonist, the UMs seems to have a pythagorean ontology. An annex of my french thesis has the title: "Church Thesis rehabilitate Pythagorism".
:-)
Could it be possible to have a notion of accessibility to parametrize or weaking the word "every" as in the sentence: " A point x in X is a limit point of S if every open set containing x contains at least one point of S different from x itself." to "A point x in X is a limit point of S if every open set , that is assessible from some S, containing x contains at least one point of S different from x itself. The idea is that S and x cannot be an infinite distance (or infinite disjoint sequence of open sets) apart.
It seems to me that this would limit the implied omniscience of the compactness criteria (via the usual axiom of choice) and it seems more consistent with the notion that an emulation does not need to be *exact* to be informative.
Perhaps. Cerrtainly open problem in comp+Theaetetus.
[SPK]
Does that not imply that the explanatory value of comp+Theaetus is partly dependent of the resolution of such a problem? If we are going to seriously consider your form of ideal monism to be correct, as opposed to some form of non-substance dualism or material monism or neutral monism, do such questions not need to be looked at with seriousness? I am very interested in ontological theories, thus my queries.
Comp gives neutral monism. It is ideal is you want the numbers to be idea, but then they are idea of God. But that move is not strictly necessary.
I don't defend mechanism, Stephen. I am a logician, I just show that mechanism and weak materialism does not work together, and I show the consistence of mechanism, by showing that the UMs can understand this already.
[SPK]
And I agree with your result, it follows unassailably from its premises.
I am just trying to get you to see that there is more that you seem to not wish to see.
[SPK]
To invoke the existence of non classical logic to throw a doubt about the universal truth of elementary statements in well defined domain, like arithmetic, would lead to complete relativism, given that you can always build some ad hoc logic/theory proving the negation of any statement, and this would make the notion of truth problematic. The contrary is true.
Relativism of that kind would be that last conclusion that I would desire! OTOH, we do need a clear notion of contextuality as illustrated by the way that words are defined in relation to other words in a dictionary.
I am problem driven. I start from the problem, and use the available math.
[SPK]
As am I. ;-) But I think that sometimes we need to look beyond the math and consider how it is that knowledge itself is possible.
Yeah, sure. That is the main object of the whole work, and Theaetetus, and all the hypostases. "Beyond the math" is done before the math, because the UDA is not in math at all. It is at the cross of cognitive and matter science. Then the UDA explains entirely why arithmetic (or combinators, ...) plays some fundamental role.
[SPK]
Might the UD itself have a topological dual? Is it sequentially compact?
A non classical logic is eventually accepted when we can find an interpretation of it in the classical framework.{SPK]
This seems to be an unnecessary prejudice! Why is the classical framework presumed to be the absolute measure of acceptability and, by implication, Reality?
No. Simplicity. Together with the need of the classical Church thesis, and our intuition of numbers. We do use the comp hypothesis, and it needs classical logic on the natural numbers. Intuitionist logic can also be used, but then the math are much more complex, and eventually we need a non trivial use of the double negation topology. It is more easy to use, like usually in math, the meta-classical background.
[SPK]
But it seems that you are assuming that our ability to have intuitions of abstractions itself has a satisfactory explanation.
I don't address that question, except with the mathematical self-reference a shadow of solution appears, perhaps.
[SPK]
Any hints that I might study?
You seem to assume that the properties of, for example, memory obtain solely from the existence of Arithmetic and that such existence is severable from the physical instantiations of memory.
I don't assume that at all. It is the result! You have to study it. It is much simpler than you seem to think.
My only assumption is that the brain works like a machine, + CT to give sense to the word machine, and to relate.
That memory exists in arithmetic is obvious, once you understand that arithmetic emulate all computations. That physical memories arise is more subtle to show, but that is the point of the whole UDA.
[SPK]
/shakes head ... Sometimes I wonder if you are choosing not to see past your formulas. :-(
This statement seems to reveal an explanation of why you believe that QM is derivative of classical logic somehow in spite of my repeated statements to the work of others that show that this is simply not possible except in a crude and non-faithful manner!
You repeatedly confuse the notion of embedding of a logic in another, and representing a logic in another. I have explained this many times, but you keep coming back on that confusion. QL cannot be faithfully extended in Boolean logic, but this does not mean that you cannot represent QL in a classical frame work (like it is done all the time; quantum mechanics is itself a classical theory).
[SPK]
How is a representation of logic A in logic B not equivalent to an embedding of A in B? Maybe I am conflating a model with a representation.
For an embedding you need some injective morphism. For a representation you need a mean to translate the theorems.QL is not embeddable in classical logic (it means, roughly that you cannot have hidden variable), but QL can be interpreted by many classical structures (lattice, modal B systems, etc.).
[SPK]
Thank you for this definition. I have been unable to find it in the literature so far.
[SPK]
A non standard truth set, like the collection of open subsets of a topological space, provided a classical sense for intuitionist logic, like a lattice of linear subspaces can provide a classical interpretation of quantum logic (indeed quantum logic is born from such structures). It might be that nature observables obeys quantum logic, but quantum physicists talk and reason in classical logic, and use classical mathematical tools to describe the non classical behavior of matter.
I agree but will point out that the use of classical logic could be merely a habit and convenience.
Classical logic allows non constructive reasoning which are obligatory in any modest theology, like the machine's theologies.Do you agree that a (mathematical) machine stop or ... do not stop, on some input. We don't need more than that.
[SPK]
A mathematical object, as I can understand it, is purely an abstraction that supervenes upon the actions of a mind to have a meaning. The particular properties of the object flow from the rules, axioms, etc. that are used to define said object and do not depend on anything else except the possibility of some instantiation of those rules, axioms, etc.
In logic, the model are the intantiations, but they are mathematical structure.
[SPK]
Might you read pages 187-193 of David Deutsch's new book, The Beginning of Infinity. He elaborates the problem that I see with this claim that you are making. I just found the argument in Deutsch's book last week and was very surprised that it is not "common sense".
[SPK]
If a "machine" is a form of mathematical structure
Better to see a machine as a relative number. It might be wriiten in sophisticated language, like quantum topology, giving them complex shape, but they are still relative numbers. This follows from the digital condition, which is assume for the machine we talk about in the comp framework.
OK.
[SPK]
then its existence is not predicated on any particular instantiation of such a machine but its properties are not defined by the mere possibility of its existence. Additionally, the notion of "stopping" or "not stopping" has a meaning that refers to a process in some way. A process cannot be reduced to a static relation between abstract entities but it can be represented by sequences of static relations. I distinguish between the representation of a process and the process itself. A map is not the territory.
Arithmetical truth is the territory. Machines and numbers are what build maps of the territory. When you say "yes" to a doctor, you are just changing a map for another. Nowhere is a confusion between map and territory, except for the fixed points, like the here and now indexical consciousness. But we can be thankful that this is possible (in computer science) because it makes the map/brain useful when relating with a probable part of the territory.
But are when maps and territories are made of the "same stuff" we have problems.
[SPK]
OTOH, if we consider the idea that we can relate simulations of a given process with the process itself, we are comparing one form of process to another, not a static set of relations to a process. I do not think of mathematical objects as static relations only, I see them more as invariant patterns that occur in a background of eternal interactions between possible aspects of Existence.
The question was: do you agree that phi_i(j) always either gives a result, or does not give a result.
If phi_i(j) can be instantiated by a topological space, yes. No, if it cannot be.
[SPK]
I think that there may be a reason why classical logics are taken as fundamental, but this reasoning is build on the intuition that a 3p "public" notion of communication can only be defined in Boolean logical terms; in other words, we observe a classical reality because that is the manner that maximally consistent collections of open sets can bisimulate each other. Bisimulation is communication between and within logical systems. If bisimulation cannot occur between a pair of logics then there is no interactions between the topological spaces dual to those logics. This gives us a way to think of seperate physical worlds. But this reasoning requires that we treat logics and topological spaces on an equal ontological footing. Logic cannot be taken as the unique ontological aspect of existence.
It follows from the step 8 of UDA that if we are machine, classical arithmetic is a theory of everything. Non classical logics are recovered in the machine's epistemologies. S4grz1 is intuitionist and the Z1* and X1* logics are type of quantum logics.
If we are some abstract static relational structure then Arithmetic is an explanation of everything?
No. If we are digital machine (physical, material, or not) then physics has to be explained by statistics on computations, viewed from an angle.
It is not an explanation at all. It is a consequence of having a brain functioning by obeying laws (UDA).
AUDA seems to illustrate that this is quite possible, given that it shows that the measure one on the computation, if it exist, give rise to a quantum like physics.
[SPK]
That remains to be proven.
We must show how a measure obtains for this result.
Maybe for an abstract and static entity, but not for an entity that needs to explain the appearance of a universe that is never only identically itself. I do not identify an arbitrary collection of static relations with Change in a decidable one to one and onto way.
Just say no to the doctor then. This means you take physical time as a primitive again, and UDA shows that this does not work if we can survive from a material brain transplant. Besides I am not sure that Change has physical sense with current physics too, nor even what you mean by that. Prigogine also believed in a basic primitive time, but he did not convince me on this.
Bruno
[SPK]
I tend to not trust anyone, especially "experts".
My ideas about time where molded by the reasoning of Hitoshi Kitada et al. You might read his papers some day.
Stephen P. King
On 30 Sep 2011, at 04:45, Stephen P. King wrote:
On 9/29/2011 2:15 PM, Bruno Marchal wrote:
On 29 Sep 2011, at 16:36, Stephen P. King wrote:
On 9/29/2011 4:03 AM, Bruno Marchal wrote:
On 28 Sep 2011, at 16:44, Stephen P. King wrote:
On 9/27/2011 10:47 AM, Bruno Marchal wrote:
On 27 Sep 2011, at 13:49, Stephen P. King wrote:
On 9/26/2011 7:56 PM, Jason Resch wrote:
<snip>
For well-defined propositions regarding the numbers I think the values are confined to true or false.
Jason
--�[SPK]
��� Not in general, unless one is only going to allow only Boolean logics to exist. There have been proven to exist logics that have truth values that range over any set of numbers, not just {0,1}. Recall the requirement for a mathematical structure to exist: Self-consistency.
Consistency is a notion applied usually to theories, or (chatty) machines, not to mathematical structures.
A theory is consistent if it does not prove some proposition and its negation. A machine is consistent if it does not assert a proposition and its negation.
[SPK]
��� Is not a machine represented mathematically by some abstract (mathematical ) structure?� I am attempting to find clarity in the ideas surrounding the notion of "machine" and how you arrive at the idea that the abstract notion of implementation is sufficient to derive the physical notion of implementation.
This follows from the UD Argument, in the digital mechanist theory. No need of AUDA or complex math to understand the necessity of this, once we accept that we can survive with (physical, material) digital machines.
[SPK]
��� Is the property of universality independent of whether or not a machine has a set of properties? What is it that determines the properties of a machine? I need to understand better your definition of the word "machine".
It is anything that can be emulated by a universal turing machines. With Church thesis, I don't have to be much more precise than that. Once you have one universal system, it emulates all possible machines, and the UD emulates them all effectively.So in any physical universe emulating a UD, we are already there, and physics has to be retrieved from some statistics on the computations.And the movie graph argument explained that the "natural" emulation of a UD made by the natural numbers through their additive and multiplicative relations is enough.
In first order logic we have G�del-Henkin completeness theorem which shows that a theory is consistent if and only if there is a mathematical structure (called model) satisfying (in a sense which can be made precise) the proposition proved in the theory.
[SPK]
��� What constraints are defined on the models by the G�del-Henkin completeness theorem? How do we separate out effective consistent first-order theories that do not have computable models?
What do you mean by computable models?
[SPK]
��� Allow me to quote several definitions: "computable functions are exactly the functions that can be calculated using a mechanical calculation device given unlimited amounts of time and storage space. " (from http://en.wikipedia.org/wiki/Computable_function).� "a computable model is one whose underlying set is decidable and whose functions and relations are uniformly computable. " (from http://arxiv.org/abs/math/0602483).
Which functions and relations? Those corresponding to the primitive terms of the theory, or all relations?If it is the first case, then this would give the standard model (in case the theory is first order arithmetic).
I am not sure I see your point.�
[SPK]
��� Could you have communicated this question to me if it was impossible to create a physical instance of the question?
Assuming comp: of course. If we are both Turing emulable, the UD, or arithmetic, emulate all our possible interactions.�
How to minds interact?
By using their material bodies, or G�del 'numbers'.
I say that they interact via bisimulation and, dually, by topological transformations between Stone-type spaces.
Like in Pratt. I have not so much problem with this. the point is that we have derive this from adition and multiplication to statified the UDA-type of constraints making it possible to explain the difference between, quanta and qualia, based on self-reference.
��� A computable model, as I understand it, could be considered as a representation of a system or structure whose properties can be determined by some process that can itself be represented as a function from the set of countable numbers to itself. This defintion seeks to abstractly represent the way that we can determine the properties of a physical system X or, equivalently, generate a finite list of operations that will create an instance of X.
?
[SPK]
Also, it is true that classical (Boolean) logic are not the only logic. There are infinitely many logics, below and above classical propositional logic. But this cannot be used to criticize the use of classical logic in some domain.
��� OK. My thought here was to show that classical (Boolean) logic is not unique and should not be taken as absolute. To do so would be a mistake similar to Kant's claim that Euclidean logic was absolute.
OK, but then why to use that fact to criticize Jason's defense of arithmetical truth independent of humans.
[SPK]
��� I am claiming a distinction between the existence of a structure and the definiteness of its properties.
I limit existence to natural numbers. The rest is numbers imagination to try to understand the numbers. "existence of a structure" has some sense in some mathematical theories, which I can believe genuine and even useful for the epistemology of numbers, but I am neutral on the nature of that existence, beyond belonging to the internal mindscape of the machine (which is really already beyond mathematics.�
[SPK]
��� Some people might think that this a bigotry of the worst kind.
Being neutral on a point is hardly bigotry.
To imagine that all that exists in limited by what a particular kind of finite entity can count, such a chauvinism!
That is different. That is a consequence of the UD Argument. It is not that we do need more than arithmetic. It is that we cannot use more than arithmetic, without automatically blurring the quanta/qualia distinction.
You forget that our method of counting is a by-product of our physics.
With comp, our physics is universal. It is the same for all entities (even the gods). It is different for only one entity (God, if that exists). This is the beauty of comp: physics becomes universal, and is based only on very few arithmetical principle.
As Deutsch explains, the physics that our universe of experience has is not unique. Different laws of physics generate differnt forms of possible counting and thus different concepts of numbers for entities existing in those universes.
This is just physicalist non sense. With comp, only geographies and histories can be different, and the arithmetical truth are geography-history independent.
It is my claim that prior to the establishment of whether or not a method of determining or deciding what the properties of a structure or system are, one can only consider the possibility of the structure or system. For example, say some proposition or sentence of a language exists. Does that existence determine the particulars of that proposition or sentence?
That is very unclear.
[SPK]
��� Does the mere existence of an unspecified sentence determine its possible meanings?
The meaning of a sentence appears before an observer appears and utter that sentence. You need a human to grasp the meaning of "the big bang" occurred, but the big bang can occur without any observer around. If not, then you do fall in solipsism.What might be true for the big bang seems even more obvious for statement like "17 is prime".
[SPK]
If it can how so? How do can we claim to be able to decide that P_i is true in the absence of a means to determine or decide what P_i means?
It can be true even if we can't decide it is. This makes sense for the arithmetical relations (but indeed it is far more complex for sets, and machine epistemology).It seems clear to me that one of the following two sentences is true, and the other one false:There is an infinity of twin primes.There is a biggest twin prime.OK?If you are OK, then you agree, by definition, with the minimal (arithmetical) realism we need to give sense to mechanism.
��� Not OK. If you (or any one that you could instruct) where unable to write those sentences, what meaning would they have?
They would have their usual 3-p meaning, like I explain above with the big-bang, or with "17" is prime.
How can we ignore the fact that symbolic, iconic or whatever form of representations, with which we communicate ideas, cannot occur absent a physical world with some definite physical laws.
But reality is independent of *our* iconic devices. That is the act of faith of any non solipsist researchers on fundamentals.
This does not mean that such as ontologically primitive, not at all. It means that one must give equal ontological weight to the appearances of physical worlds in the 1p as we give to the abstract mathematical entities that they are implementing.
Comp implies this at some hiher level, but discard it at the roots: Numbers implement the computational histories/dreams, from which the appearance of matter emerges, from which dreams coalesce into first person sharable dreams, from whioch things like hulmans appears.
I invite you to read Bertrand Russell's article on neutral monism�http://cco.cambridge.org/extract?id=ccol0521631785_CCOL0521631785A012.� He has a much better command of the explanation of this idea than I do. I am just a curious student studying my books and asking questions.
No problem with neutral monism. The comp arithmeticalism is a neutral monism. It explains how the coupling matter/consciousness emerges from numbers (and + and *).
��� How do you know the meaning of these word "Unicorn"? Is the meaning of the word "Unicorn" something that that arises simply from the existence of sequence of symbols? is not meaning not something like a map between some set of properties instantiated entity and some set of instances of those properties in other entities? Consider an entity X that had a set of properties x_i that could not be related to those of any other entity? Would this prevent the existence of X?
The existence of X is the necessary possibility of X, []<>X.
I like that. As you know X ->[]<>X (which i write �p ->�[]<>X) is the initial abstract equation of physics already gathered by the interview with the LUM. here X is a sigma_1 sentence, and []x means Bx & Dt, with B = G�del's beweisbar (and <> = ~[]~, and D = ~B~, as usual).
Does a unicorn exists. I don't know, and I am not sure "unicorn" is well defined, nor "exist" in this case. Same for the moon, to be sure.
[SPK]
��� Surely it can exist, but what properties does it have? We simply do not know.
If comp +Theaetus is correct, you have to distinguish physical existence, which is of the type []<>#, and existence, which is of the type "Ex ... x...". I will use the modal box [] and diamond <> fro the intelligible hypostases ([]X = BX & DX).
[SPK]
��� It seems that we have very different ideas of the meaning of the word Existence. "Ex ... x..." seems to be a denotative definition and thus is not neutral with respect to properties. I may not comprehend� you thoughts on this. Do you have a concept for "the totality of all that exists"? Would such be unnamable for you? It is for me. As I see it, existence itself is the neutral primitive ground of all things, abstract and concrete. Perhaps my philosophy is more like dual-aspect monism than neutral monism.
��� I found several new Goldblatt papers and will read for a while...
All treatises on any non classical logic used classical (or much more rarely intuitionistic) logic at the meta-level. You will not find a book on fuzzy logic having fuzzy theorems, for example. Non classical logics have multiple use, which are not related with the kind of ontic truth we are looking for when searching a TOE.
[SPK]
��� Of course fuzzy logic does not have fuzzy theorem, that could be mistaking the meaning of the word "fuzzy" with the meaning of the word "ambiguous". I have been trying to establish the validity of the idea that it is the rules (given as axioms, etc) that are used to define a given mathematical structure, be it a model, or an algebra, etc. But I think that one must be careful that the logical structure that one uses of a means to define ontic truths is not assumed to be absolute unless very strong reasons can be proven to exist for such assumptions.
Usually non classical logic have epistemic or pragmatic classical interpretations, or even classical formulation, like the classical modal logic S4 which can emulate intuitionistic logic, or the Brouwersche modal logic B, which can emulate weak quantum logic. This corresponds to the fact that intuitionist logic might modelize constructive provability, and quantum logic modelizes observability, and not the usual notion of classical truth (as used almost everywhere in mathematics).
[SPK]
��� I use the orthocomplete lattices as a representation of quantum logic. My ideas are influenced by the work of Svozil, Calude� and von Benthem, and others on this. I am not sure of the definition of "weak quantum logic" as you use it here.
Svozil, Calude and van Benthem thought on the subject are very good. Weak quantum logic is the logic of sublattice of ortholattices, like in the paper of Goldblatt that I have often refer to you. Basically it is quantum logic without the orthomodularity axiom. It does not distinguish finite dimensional pre-Hilbert space from Hilbert space, for example.
[SPK]
��� This paper http://www.jstor.org/pss/2274172 ? It seems to me that the distributivity axiom would not make the same distinction either, although Hilbert space is defined in terms of a linear algebra on a vector space. Consider this paper's abstract.
http://www.google.com/url?sa=t&rct=j&q=orthomodularity%20axiom&source=web&cd=5&sqi=2&ved=0CDgQFjAE&url=http%3A%2F%2Fm3k.grad.hr%2Fpapers-ps-pdf%2Fquantum-logic%2F1998-helv-phys-acta.pdf&ei=N3SETo2yFYGztwfLiYU0&usg=AFQjCNHal3UDb6B-MATSt1hloWFhSNVCnw&sig2=Fl7ESJLpFZ9qj8c8YU8S-w&cad=rja
"We show that binary orthologic becomes either quantum or classical logic when nothing but modus
ponens rule is added to it, depending on the kind of the operation of implication used. We also show that
in the usual approach the rule characterizes neither quantum nor classical logic. The diff erence turns out
to stem from the chosen valuation on a model of a logic. Thus algebraic mappings of axioms of standard
quantum logics would fail to yield an orthomodular lattice if a unary - as opposed to binary - valuation
were used. Instead, non-orthomodular nontrivial varieties of orthologic are obtained. We also discuss the
computational efficiency of the binary quantum logic and stress its importance for quantum computation
and related algorithms."
��� How can we even consider the distinction of one form of abstract structure, such as logical algebras or lattices, from another without there existing a means to generate instantiations of the two? This question goes to the heart of my skepticism of your result.
I don't see any relation between the quote, and your comment.�And what do you mean by instantiation? Do you mean physical instantiation, or mathematical instantiation. From inside, UDA shows that universal machine (even physically instantiated one, even assuming primitive matter) cannot distinguish them.�
[SPK][SPK]
��� OK, but do you not see that this result might explain the conflation of physical and mathematical notions of implementation if one is thinking only according to UDA? I see them as different because I do not think in symbolic forms. It is a disability of� sequential brain processing and memory (dyslexia) that prevents my delusion. How ironic.
I feel sorry for your problem. It remains amazing how much links you give on purely symbolic reasoning.�
��� Once I have constructed a mental representation of the subject of a reasoning or concept I can use the symbolic representations in a denotative capacity. This is how we dyslexics overcome our disability. :-)
My result is: mechanism entails immateralism (matter can exist but as no more any relation with consciousness, and so is eliminated with the usual weak occam principle). This should be a problem for you if you want to keep both mechanism and weak materialism, but why do you want to do that. On the contrary, mechanism makes the laws of physics much more solid and stable, by providing an explanation relying only on diophantine addition and multiplication.
[SPK]
��� I reject all form of monism except neutral monism. Existence itself is the only primitive.
In what sense would mechanism, after UDA, not be a neutral monism.When you use the word "existence" without saying what you assume to exist, it look like the joke "what is the difference between a raven?".
[SPK]
��� The totality of all that exists, it merely exists. Prior to the specification of properties, even distinctions themselves, there is only existence. Existence is not a property such as Red, two or heavy. It has no extension or form in itself but is the possibility to be and have all properties.
[SPK]
[SPK]
��� One question regarding the emulations. If one where considering only finite emulations of a quantum logic (such as how a classical approximation of a QM system could be considered), how might one apply the Tychonoff, Heine�Borel definition or Bolzano�Weierstrass criterion of compactness to be sure that compactness obtain for the models? If we use these compactness criteria, is it necessary that the collection of open sets that is used in complete in an absolute sense? Could it be that we have a way to recover the appearence of the axiom of choice or the ultrafilter lemma?
Hard and premature questions.
��� But do we not decide whether or not to pursue a conjecture by the implications of the conjecture? The questions that I am asking here are questions of the ability of the idea to give us an explanatory narrative that we can use to reason about our world. You are, with your result, proposing a result that implies an ontological theory: that Reality is, at its primitive level, purely abstract. This seems to be more of an echo of the ideas of Pythagoras than those of Plato...
Sure! �Like the neoplatonist, the UMs seems to have a pythagorean ontology. An annex of my french thesis has the title: "Church Thesis rehabilitate Pythagorism".
��� :-)
It is a key point.�
��� Could it be possible to have a notion of accessibility to parametrize or weaking the word "every" as in the sentence: " A point x in X is a limit point of S if every open set containing x contains at least one point of S different from x itself." to "A point x in X is a limit point of S if every open set , that is assessible from some S, containing x contains at least one point of S different from x itself. The idea is that S and x cannot be an infinite distance (or infinite disjoint sequence of open sets) apart.
��� It seems to me that this would limit the implied omniscience of the compactness criteria (via the usual axiom of choice) and it seems more consistent with the notion that an emulation does not need to be *exact* to be informative.
Perhaps. Cerrtainly open problem in comp+Theaetetus.
[SPK]
��� Does that not imply that the explanatory value of comp+Theaetus is partly dependent of the resolution of such a problem? If we are going to seriously consider your form of ideal monism to be correct, as opposed to some form of non-substance dualism or material monism or neutral monism, do such questions not need to be looked at with seriousness? I am very interested in ontological theories, thus my queries.
Comp gives neutral monism. It is ideal is you want the numbers to be idea, but then they are idea of God. But that move is not strictly necessary.
I don't defend mechanism, Stephen. I am a logician, I just show that mechanism and weak materialism does not work together, and I show the consistence of mechanism, by showing that the UMs can understand this already.
[SPK]
��� And I agree with your result, it follows unassailably from its premises.
That is nice, but then I am not sure to make sense of your point.
I am just trying to get you to see that there is more that you seem to not wish to see.
Which are?
[SPK]
��� Numbers and arithmetic presuppose a specific meaning, valuation and relation. This implies, in my reasoning, that they are not primitive. You seem to assume that they are objects in the mind of God, making God = Existence. I disagree with this thinking.
�
[SPK]
To invoke the existence of non classical logic to throw a doubt about the universal truth of elementary statements in well defined domain, like arithmetic, would lead to complete relativism, given that you can always build some ad hoc logic/theory proving the negation of any statement, and this would make the notion of� truth problematic. The contrary is true.
��� Relativism of that kind would be that last conclusion that I would desire! OTOH, we do need a clear notion of contextuality as illustrated by the way that words are defined in relation to other words in a dictionary.
I am problem driven. I start from the problem, and use the available math.
[SPK]
��� As am I. ;-) But I think that sometimes we need to look beyond the math and consider how it is that knowledge itself is possible.
Yeah, sure. That is the main object of the whole work, and Theaetetus, and all the hypostases. "Beyond the math" is done before the math, because the UDA is not in math at all. It is at the cross of cognitive and matter science. Then the UDA explains entirely why arithmetic (or combinators, ...) plays some fundamental role.
[SPK]
��� Might the UD itself have a topological dual? Is it sequentially compact?
Could you define to me what you mean by topological dual of a number, or a program?
[SPK]
��� I do not recognize the idea that a number or a program has a meaning isolate from all else. I do not understand your theory of meaningfulness. How does meaningfulness arise in your thinking? I use a non-well founded set type Dictionary model and have discussed it before.
A non classical logic is eventually accepted when we can find an interpretation of it in the classical framework.{SPK]
��� This seems to be an unnecessary prejudice! Why is the classical framework presumed to be the absolute measure of acceptability and, by implication, Reality?
No. Simplicity. Together with the need of the classical Church thesis, and our intuition of numbers. We do use the comp hypothesis, and it needs classical logic on the natural numbers. Intuitionist logic can also be used, but then the math are much more complex, and eventually we need a non trivial use of the double negation topology. It is more easy to use, like usually in math, the meta-classical background.�
[SPK]
��� But it seems that you are assuming that our ability to have intuitions of abstractions itself has a satisfactory explanation.
I don't address that question, except with the mathematical self-reference a shadow of solution appears, perhaps.
[SPK]
��� Any hints that I might study?
I have never stop to give references on this, beyond my own work. See the name Boolos, Smorynski, Smullyan in my papers and books, or in my URL.�
What is it that you don't understand in the second part of the sane paper.
[SPK]
��� I do not understand how you ignore the fact that one must have a means to implement a set of distinguishable symbols, configuration of chalk mark on slate, etc. to denote and connote an abstraction. It is as if you presuppose physicality without giving it credit for what it does. I do not know what else to say now to make this idea more clear.
You seem to assume that the properties of, for example, memory obtain solely from the existence of Arithmetic and that such existence is severable from the physical instantiations of memory.
I don't assume that at all. It is the result! You have to study it. It is much simpler than you seem to think.�
My only assumption is that the brain works like a machine, + CT to give sense to the word machine, and to relate.�
That memory exists in arithmetic is obvious, once you understand that arithmetic emulate all computations. That physical memories arise is more subtle to show, but that is the point of the whole UDA.
[SPK]
��� /shakes head ... Sometimes I wonder if you are choosing not to see past your formulas. :-(
?
This statement seems to reveal an explanation of why you believe that QM is derivative of classical logic somehow in spite of my repeated statements to the work of others that show that this is simply not possible except in a crude and non-faithful manner!
You repeatedly confuse the notion of embedding of a logic in another, and representing a logic in another. I have explained this many times, but you keep coming back on that confusion. QL cannot be faithfully extended in Boolean logic, but this does not mean that you cannot represent QL in a classical frame work (like it is done all the time; quantum mechanics is itself a classical theory).
[SPK]
��� How is a representation of logic A in logic B not equivalent to an embedding of A in B? Maybe I am conflating a model with a representation.
For an embedding you need some injective morphism. For a representation you need a mean to translate the theorems.
QL is not embeddable in classical logic (it means, roughly that you cannot have hidden variable), but QL can be interpreted by many classical structures (lattice, modal B systems, etc.).�
[SPK]
��� Thank you for this definition. I have been unable to find it in the literature so far.
[SPK]
A non standard truth set, like the collection of open subsets of a topological space, provided a classical sense for intuitionist logic, like a lattice of linear subspaces can provide a classical interpretation of quantum logic (indeed quantum logic is born from such structures). It might be that nature observables obeys quantum logic, but quantum physicists talk and reason in classical logic, and use classical mathematical tools to describe the non classical behavior of matter.
��� I agree but will point out that the use of classical logic could be merely a habit and convenience.
Classical logic allows non constructive reasoning which are obligatory in any modest theology, like the machine's theologies.Do you agree that a (mathematical) machine stop or ... do not stop, on some input. We don't need more than that.
[SPK]
��� A mathematical object, as I can understand it, is purely an abstraction that supervenes upon the actions of a mind to have a meaning. The particular properties of the object flow from the rules, axioms, etc. that are used to define said object and do not depend on anything else except the possibility of some instantiation of those rules, axioms, etc.
In logic, the model are the intantiations, but they are mathematical structure.
[SPK]
��� Might you read pages 187-193 of David Deutsch's new book, The Beginning of Infinity. He elaborates the problem that I see with this claim that you are making. I just found the argument in Deutsch's book last week and was very surprised that it is not "common sense".
Physicist seems not to have the notion of models, and use that term where logician use the term "theory". Roughly speaking, for a logician "model" is for "a reality". I remind you also that Deutch advocates physicalism, and so, if you get the UDA as you said, you know that Deustch physicalism is incoherent with digital mechanism (which he advocates in FOR).
[SPK]
��� I wish that you would write more addressing this critique of Deutsch's argument.
[SPK]
If a "machine" is a form of mathematical structure
Better to see a machine as a relative number. It might be wriiten in sophisticated language, like quantum topology, giving them complex shape, but they are still relative numbers. This follows from the digital condition, which is assume for the machine we talk about in the comp framework.
��� OK.
[SPK]
then its existence is not predicated on any particular instantiation of such a machine but its properties are not defined by the mere possibility of its existence. Additionally, the notion of "stopping" or "not stopping" has a meaning that refers to a process in some way. A process cannot be reduced to a static relation between abstract entities but it can be represented by sequences of static relations. I distinguish between the representation of a process and the process itself. A map is not the territory.
Arithmetical truth is the territory. Machines and numbers are what build maps of the territory. When you say "yes" to a doctor, you are just changing a map for another. Nowhere is a confusion between map and territory, except for the fixed points, like the here and now indexical consciousness. But we can be thankful that this is possible (in computer science) because it makes the map/brain useful when relating with a probable part of the territory.
��� But are when maps and territories are made of the "same stuff" we have problems.
Not necessarily. Or you take the word stuff too literally perhaps.
[SPK]
��� I used the word 'stuff" in quotes so that it would not be taken as literal.
��� OTOH, if we consider the idea that we can relate simulations of a given process with the process itself, we are comparing one form of process to another, not a static set of relations to a process. I do not think of mathematical objects as static relations only, I see them more as invariant patterns that occur in a background of eternal interactions between possible aspects of Existence.
The question was: do you agree that phi_i(j) always either gives a result, or does not give a result.
[SPK]
��� If phi_i(j) can be instantiated by a topological space, yes. No, if it cannot be.
You can use Scott topology to modelize computations. Stopping programs will correspond to fixed point transformations.But my question was more easy, and can be recasted in physical terms: does a machine stop or not stop (accepting a robust physical universe, and no accidental asteroid destructing the machine)?
[SPK]
��� OK, I still do not comprehend how you can say this and still be a ideal monist. I am tired.
Onward!
Stephen
[SPK]
I think that there may be a reason why classical logics are taken as fundamental, but this reasoning is build on the intuition that a 3p "public" notion of communication can only be defined in Boolean logical terms; in other words, we observe a classical reality because that is the manner that maximally consistent collections of open sets can bisimulate each other. Bisimulation is communication between and within logical systems. If bisimulation cannot occur between a pair of logics then there is no interactions between the topological spaces dual to those logics. This gives us a way to think of seperate physical worlds. But this reasoning requires that we treat logics and topological spaces on an equal ontological footing. Logic cannot be taken as the unique ontological aspect of existence.
It follows from the step 8 of UDA that if we are machine, classical arithmetic is a theory of everything. Non classical logics are recovered in the machine's epistemologies. S4grz1 is intuitionist and the Z1* and X1* logics are type of quantum logics.
��� If we are some abstract static relational structure then Arithmetic is an explanation of everything?
No. If we are digital machine (physical, material, or not) then physics has to be explained by statistics on computations, viewed from an angle.
It is not an explanation at all. It is a consequence of having a brain functioning by obeying laws (UDA).
AUDA seems to illustrate that this is quite possible, given that it shows that the measure one on the computation, if it exist, give rise to a quantum like physics.
[SPK]
��� That remains to be proven.
That has been proved.
We must show how a measure obtains for this result.
That has been shiwn possible, and promising result have been found (where some people deny any sense in this for many years).�That it remains open problems is the least we can say. The goal of the work was in the formulation of the (Mind-body) problem, and in its conceptual solution, not really in the complete solution, which might take some times, we never known.�
Maybe for an abstract and static entity, but not for an entity that needs to explain the appearance of a universe that is never only identically itself. I do not identify an arbitrary collection of static relations with Change in a decidable one to one and onto way.
Just say no to the doctor then. This means you take physical time as a primitive again, and UDA shows that this does not work if we can survive from a material brain transplant. Besides I am not sure that Change has physical sense with current physics too, nor even what you mean by that. Prigogine also believed in a basic primitive time, but he did not convince me on this.
Bruno
[SPK]
��� I tend to not trust anyone, especially "experts".
Good!
My ideas about time where molded by the reasoning of Hitoshi Kitada et al. You might read his papers some day.
We have already discuss this. It makes such a view of reality epistemologically inconsistent with comp. If you grasped UDA, you should know that. I take it that, like Craig, you are betting on the falsity of comp, and I have no problem with that.
Bruno
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Bruno Marchal
On 9/30/2011 5:45 AM, Bruno Marchal wrote:[SPK]If comp +Theaetus is correct, you have to distinguish physical existence, which is of the type []<>#, and existence, which is of the type "Ex ... x...". I will use the modal box [] and diamond <> fro the intelligible hypostases ([]X = BX & DX).
It seems that we have very different ideas of the meaning of the word Existence. "Ex ... x..." seems to be a denotative definition and thus is not neutral with respect to properties. I may not comprehend you thoughts on this.
Do you have a concept for "the totality of all that exists"?
Would such be unnamable for you? It is for me.
As I see it, existence itself is the neutral primitive ground of all things, abstract and concrete. Perhaps my philosophy is more like dual-aspect monism than neutral monism.
[SPK]
Once I have constructed a mental representation of the subject of a reasoning or concept I can use the symbolic representations in a denotative capacity. This is how we dyslexics overcome our disability. :-)
My result is: mechanism entails immateralism (matter can exist but as no more any relation with consciousness, and so is eliminated with the usual weak occam principle). This should be a problem for you if you want to keep both mechanism and weak materialism, but why do you want to do that. On the contrary, mechanism makes the laws of physics much more solid and stable, by providing an explanation relying only on diophantine addition and multiplication.
[SPK]
I reject all form of monism except neutral monism. Existence itself is the only primitive.
In what sense would mechanism, after UDA, not be a neutral monism.When you use the word "existence" without saying what you assume to exist, it look like the joke "what is the difference between a raven?".
[SPK]
The totality of all that exists, it merely exists.
Prior to the specification of properties, even distinctions themselves, there is only existence. Existence is not a property such as Red, two or heavy. It has no extension or form in itself but is the possibility to be and have all properties.
[SPK]
Numbers and arithmetic presuppose a specific meaning, valuation and relation.
This implies, in my reasoning, that they are not primitive.
You seem to assume that they are objects in the mind of God, making God = Existence. I disagree with this thinking.
[SPK]
Could you define to me what you mean by topological dual of a number, or a program?
I do not recognize the idea that a number or a program has a meaning isolate from all else. I do not understand your theory of meaningfulness. How does meaningfulness arise in your thinking? I use a non-well founded set type Dictionary model and have discussed it before.
I have never stop to give references on this, beyond my own work. See the name Boolos, Smorynski, Smullyan in my papers and books, or in my URL.
What is it that you don't understand in the second part of the sane paper.
[SPK]
I do not understand how you ignore the fact that one must have a means to implement a set of distinguishable symbols, configuration of chalk mark on slate, etc. to denote and connote an abstraction. It is as if you presuppose physicality without giving it credit for what it does. I do not know what else to say now to make this idea more clear.
[SPK]
Physicist seems not to have the notion of models, and use that term where logician use the term "theory". Roughly speaking, for a logician "model" is for "a reality". I remind you also that Deutch advocates physicalism, and so, if you get the UDA as you said, you know that Deustch physicalism is incoherent with digital mechanism (which he advocates in FOR).
I wish that you would write more addressing this critique of Deutsch's argument.
[SPK]Arithmetical truth is the territory. Machines and numbers are what build maps of the territory. When you say "yes" to a doctor, you are just changing a map for another. Nowhere is a confusion between map and territory, except for the fixed points, like the here and now indexical consciousness. But we can be thankful that this is possible (in computer science) because it makes the map/brain useful when relating with a probable part of the territory.
But are when maps and territories are made of the "same stuff" we have problems.
Not necessarily. Or you take the word stuff too literally perhaps.
[SPK]
I used the word 'stuff" in quotes so that it would not be taken as literal.
[SPK]
You can use Scott topology to modelize computations. Stopping programs will correspond to fixed point transformations.But my question was more easy, and can be recasted in physical terms: does a machine stop or not stop (accepting a robust physical universe, and no accidental asteroid destructing the machine)?
OK, I still do not comprehend how you can say this and still be a ideal monist. I am tired.
David Nyman
> They are ontologically primitive, in the sense that ontologically they are
> the only things which exist. even computations don't exist in that primitive
> sense. Computations already exists only relationally. I will keep saying
> that computations exists, for pedagogical reasons. For professional
> logicians, I make a nuance, which would look like total jargon in this list.
I've been following this discussion, though not commenting (I don't
understand all of it). However, your remark above caught my eye,
because it reminded me of something that came up a while back, about
whether reductive explanations logically entail elimination of
non-primitive entities. I argued that this is their whole point;
Peter Jones disputed it. Your comment (supporting my view, I think)
was that reductionism was necessarily ontologically eliminative,
though of course not epistemologically so. Indeed this seemed to me
uncontroversial, in that the whole point of a reductionist program is
to show how all references to compound entities can be replaced by
more primitive ones.
Your remark above seems now to be making a similar point about
arithmetical "reductionism" in the sense that, presumably,
computations can analogously (if loosely) be considered compounds of
arithmetical primitives, a point that had indeed occurred to me at the
time. If so, what interests me is the question that inspired the older
controversy. If the primitives of a given ontology are postulated to
be all that "really" exist, how are we supposed to account for the
apparent "existence" of compound entities? If the supposedly
fundamental underlying mechanism is describable (in principle)
entirely at the level of primitives, there would appear to be no need
of any such further entities, and indeed Occam would imply that they
should not be hypothesised. Yet the bald fact remains that this is
not how things appear to us. So should such compound appearances be
considered entirely a matter of epistemology? IOW, is the
first-person - the "inside" view - in some sense the necessary arena -
and the sole explanation - for the emergence of anything at all beyond
the primitive ontological level?
David
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Stephen P. King
I have been attempting to ask a similar question, but my words were
failing me. What is the necessity of the 1p? AFAIK, it seems that
because it is possible. This is what I mean by existence = []<>. But
does this line of reasoning, arithmetical reductionism, eventually fall
into the abyss of infinite regress or loop back to the 1p for a means to
define itself? How can we be sure that we are assuming a primitive that
is only a artifact of the limits of our imagination? Why are we so sure
that there is a "primitive" in the well founded sense?
Onward!
Stephen
>> On 30 Sep 2011, at 13:44, Stephen P. King wrote:
>>
>> On 9/30/2011 5:45 AM, Bruno Marchal wrote:
>>
>> If comp +Theaetus is correct, you have to distinguish physical existence,
>> which is of the type []<>#, and existence, which is of the type "Ex ...
>> x...". I will use the modal box [] and diamond<> fro the intelligible
>> hypostases ([]X = BX& DX).
David Nyman
> I have been attempting to ask a similar question, but my words were
> failing me. What is the necessity of the 1p? AFAIK, it seems that because it
> is possible. This is what I mean by existence = []<>. But does this line of
> reasoning, arithmetical reductionism, eventually fall into the abyss of
> infinite regress or loop back to the 1p for a means to define itself? How
> can we be sure that we are assuming a primitive that is only a artifact of
> the limits of our imagination? Why are we so sure that there is a
> "primitive" in the well founded sense?
Well, the question I'm asking has, I think, the same implications
regardless of whatsoever you take to be "primitive". The reason for
this has to do with the process of reduction itself: having followed
the path of "reducing" any and all narratives about the world to those
consisting solely of some maximally-reduced entities and their
primitive relations, we hoped finally to get to grips with some
definitive account of the "real". But the following problem then
presents itself: what is supposed to be the ontological status of the
"non-reduced" narratives? They appear to have become ontologically
redundant (i.e. in a strong sense, they don't exist, just as a house
has no ontological status independent of the bricks that constitute
it). But, contra this, they manifestly DO still exist, as we would
say, "epistemologically".
Well, one way of dealing with inconvenient truths of this sort is by
ignoring them. And so we can try to sustain the view, where it suits
our purposes, that non-primitive phenomena of certain kinds ("qualia"
for example) really don't exist, however much they may "seem" to. The
problem is that this is insufficiently radical: reductive analysis is
an irresistible ontological acid, and more than the merely "illusory"
must succumb to its dissolving power. Once it has done its work, what
lies revealed to our horrified gaze is - not a world of still somewhat
familiar "primary" macroscopic entities and events, merely shorn of
their illusory "secondary" properties - but only the starkest
landscape of the most primitive entities in their most fundamental
relations. Or rather, this is what CANNOT now be revealed, because
any possible subject of such revelation must disappear in the same
ontological catastrophe as its possible objects of knowledge. Hence,
eliminativism of this sort turns out to be more than simply and
egregiously question-begging. In effect it is a most perverse species
of attempted metaphysical grand larceny: it tries to grab with both
hands everything it has just pilfered from reality.
The only route out of this impasse seems to be to accept that the
aspects of reality that we label "epistemological" must be considered
as real (i.e. as relevant to any account of what exists) as those we
are pleased to call "primitively ontological". Bruno indeed has
sometimes referred to this aspect as the "ontological first-person".
For myself, I have remarked on the need to consider equally two
"counter-poles" of the real: the analytic and the integrative, neither
of which can intelligibly be dispensed with. In any case, failure to
take considerations of this sort into account, leads, I think, to much
of the confusion that arises in these discussions about what "really
exists".
David
Bruno Marchal
On 30 September 2011 16:55, Bruno Marchal <mar...@ulb.ac.be> wrote:They are ontologically primitive, in the sense that ontologically they arethe only things which exist. even computations don't exist in that primitivesense. Computations already exists only relationally. I will keep sayingthat computations exists, for pedagogical reasons. For professionallogicians, I make a nuance, which would look like total jargon in this list.
I've been following this discussion, though not commenting (I don't
understand all of it). However, your remark above caught my eye,
because it reminded me of something that came up a while back, about
whether reductive explanations logically entail elimination of
non-primitive entities. I argued that this is their whole point;
Peter Jones disputed it. Your comment (supporting my view, I think)
was that reductionism was necessarily ontologically eliminative,
though of course not epistemologically so.
Indeed this seemed to me
uncontroversial, in that the whole point of a reductionist program is
to show how all references to compound entities can be replaced by
more primitive ones.
Your remark above seems now to be making a similar point about
arithmetical "reductionism" in the sense that, presumably,
computations can analogously (if loosely) be considered compounds of
arithmetical primitives, a point that had indeed occurred to me at the
time. If so, what interests me is the question that inspired the older
controversy. If the primitives of a given ontology are postulated to
be all that "really" exist, how are we supposed to account for the
apparent "existence" of compound entities?
If the supposedly
fundamental underlying mechanism is describable (in principle)
entirely at the level of primitives, there would appear to be no need
of any such further entities, and indeed Occam would imply that they
should not be hypothesised.
Yet the bald fact remains that this is
not how things appear to us.
So should such compound appearances be
considered entirely a matter of epistemology?
IOW, is the
first-person - the "inside" view - in some sense the necessary arena -
and the sole explanation - for the emergence of anything at all beyond
the primitive ontological level?
David Nyman
> But UDA shows (I think) that matter and consciousness are first
> person collective constructs of all the numbers.
Yes, I agree. But my general point was that even in terms of
physicalism, the way matter ordinarily "appears" to the (unexplained)
first person is very obviously not in terms of its supposed material
primitives. When we seek an explanation for such non-primitive
experiential constructs, we look for appropriate compound concepts
that in turn are expected to cash out, ultimately, in terms of these
selfsame primitives. But, because of this very process of
explanation, such constructs, considered at the level of the
primitives that exhaustively comprise them, are exposed as unnecessary
supplementary hypotheses. They are needed to justify appearances, not
to provide unlooked-for additional influence over what, ex hypothesi,
are already "primitive", self-sufficient mechanisms. Their demand for
attention stems exclusively from the manifest fact that such things
*appear to us*.
Consequently, unless one (unintelligibly) attempts to deny such
appearances, despite relying on them for the very explanations in
question, such "conceptual realities" must be accepted as having some
distinct existence (even if only "for us") over and above the
primitives of which they are "composed". So matter seems this
(strong) sense to be "a first person collective construct" even under
the primitive assumptions of physicalism. One may call this construct
epistemological reality, or consciousness, or the first-person. But
whatever one calls it, subtracting it leaves nothing but a barren
primitive arena; one which, notwithstanding this, continues, at its
"own level", to do exactly what it always did. This is the zombie
argument writ large, except that here the "zombie" stands revealed as
merely an undifferentiated and uninterpreted primitive background.
Consequently, in my view, denial of a distinct first person ontology
ought to be seen as having the consequence of radical reduction of the
remainder to some such arena of primitives and their relations,
independent of any metaphysical postulate of their fundamental nature.
Hence, such denial is unintelligible.
David
Bruno Marchal
On 01 Oct 2011, at 17:42, David Nyman wrote:
> On 1 October 2011 14:50, Bruno Marchal <mar...@ulb.ac.be> wrote:
>
>> But UDA shows (I think) that matter and consciousness are first
>> person collective constructs of all the numbers.
>
> Yes, I agree. But my general point was that even in terms of
> physicalism, the way matter ordinarily "appears" to the (unexplained)
> first person is very obviously not in terms of its supposed material
> primitives.
I agree. That can be related to the weakness of the physicalist
approach.
I will try to answer in my other comment why this does not apply to
digital mechanism (DM).
In a sense, you remark does apply to DM, and I refer to it sometimes
by the 0,0001% of consciousness that DM cannot explain. Then point
will be that we (and machines) can explain why IF mechanism is true,
there must remain something which just cannot be explained, and this
without postulating any new first person primitive experience.
You put your finger on the crux of the difficulty of the mind-body
problem.
> When we seek an explanation for such non-primitive
> experiential constructs, we look for appropriate compound concepts
> that in turn are expected to cash out, ultimately, in terms of these
> selfsame primitives.
Not necessarily. Consciousness does not need to be a compound things.
It is here that consciousness, as a notion, differ from the nameable
constructs; like prime numbers, universal numbers, etc. With
mechanism, we can relate consciousness with modal qualitative, and non
compounded notion, like arithmetical truth, which can already be said
not compounded for any machine approaching it closely. Machines just
lacks the vocabulary here: there are none.
> But, because of this very process of
> explanation, such constructs, considered at the level of the
> primitives that exhaustively comprise them, are exposed as unnecessary
> supplementary hypotheses.
I see what you mean. But they are implicit in the belief that our
axioms makes sense. This is the implicit (and often unconscious)
religious belief of any scientist. We still have to bet that our
theories make sense, despite we know that no public theories can
provide by itself such a sense. We are using implicitly, at the very
moment we suggest (any) theory, an assumption of self-consistency, or
an assumption that there is something real. That reality is not
compounded, and cannot be reduced into its components, *by us*. Some
alien might be able to do this for us, like we can do it for simpler
machine than us, but those aliens will not been able to do this for
themselves. Colin McGuin is right: consciousness need some amount of
mysterianism.
> They are needed to justify appearances, not
> to provide unlooked-for additional influence over what, ex hypothesi,
> are already "primitive", self-sufficient mechanisms. Their demand for
> attention stems exclusively from the manifest fact that such things
> *appear to us*.
That is the heart of the qualia problem. You single out the 0,0001% of
consciousness that mechanism cannot explain by the conscious entities
themselves, *for themselves*. But machine can understand why it has to
be like that, once they bet that they are machines. And this implies
that we cannot explain completely how mechanism work, and why
mechanism does need some act of faith in the case we use it (in
practice, or in theory). That's the key reason why mechanism *is* a
theology.
>
> Consequently, unless one (unintelligibly) attempts to deny such
> appearances, despite relying on them for the very explanations in
> question, such "conceptual realities" must be accepted as having some
> distinct existence (even if only "for us") over and above the
> primitives of which they are "composed".
They will be distinct in the sense that they need, from the part of
the machine, an (instinctive) bet in a reality. With mechanism, the
bet in arithmetical truth (or more weakly self-consistency) is enough,
despite or thanks to the fact that this cannot be an entirely
intelligible act. But the machine can describe it at some metalevel,
and that is what is done with the internal modal logics.
> So matter seems this
> (strong) sense to be "a first person collective construct" even under
> the primitive assumptions of physicalism.
Yes. But this shows physicalism being contradictory or eliminativist.
Nice point.
> One may call this construct
> epistemological reality, or consciousness, or the first-person. But
> whatever one calls it, subtracting it leaves nothing but a barren
> primitive arena; one which, notwithstanding this, continues, at its
> "own level", to do exactly what it always did. This is the zombie
> argument writ large, except that here the "zombie" stands revealed as
> merely an undifferentiated and uninterpreted primitive background.
> Consequently, in my view, denial of a distinct first person ontology
> ought to be seen as having the consequence of radical reduction of the
> remainder to some such arena of primitives and their relations,
> independent of any metaphysical postulate of their fundamental nature.
> Hence, such denial is unintelligible.
Not really, even for a physicalist. Because my point above explain why
for machine, their consciousness will appear to be both "ontologically
real" yet quite distinct from anything postulated as primitive in the
theory. The fact that it is not will seem, rightly, to be
unexplainable by the machine, but the non-explainability, betting on
mechanism (and not on physicalism), can be explained by the machine.
It is necessarily mysterious, and it is necessary related to the
global picture which has to be simple (not compounded, like Plotinus'
one actually) and which has to be transcendental, and quite distinct
from any intelligible object the machine can meet or imagine.
I think that this is the big discovery made by Plotinus: reality as a
whole has to be distinct that anything which is real or being. That is
why Plotinus explain that we need the ONE, and it has to be above the
realm of the intelligible (even of the divine intelligible). he dares
to say that God is not a being, or even that it does not exist
(meaning he does not belong to th realm of the intelligible).
Put it more simply, that is why we need a notion of god, and why
mechanism make theology the fundamental science.
You can *almost* define it by what makes possible the distinction
between the first and third person, but again, with mechanism this is
"only" an epistemological distinction, indeed it is the distinction
between believing p, and believing p when p is true. Now, the machine
cannot even define such a notion of "truth" in a way encompassing
herself completely. But a rich LUMs can do this for a less rich LUMs,
and extrapolating it on herself, but this is necessarily at her own
risk and peril. The fact that it might seems to work (like surviving
with an artificial brain) will remain like an unintelligible mystery
for the machine.
Mechanism is very like Plotinian theology. To be short, only
intelligible ideas exist [only numbers and definable relations exist].
God and matter does NOT exist, but they do exist epistemologically.
And they are quite distinct for what really exist. This does not work
for a physicalist, because he want to avoid that GOD, and make the
global picture a compound of the elementary things: he want a universe
composed of material stuff, but that cannot work if we want maintain
the existence (even if epistemological) of first person, and that is
why honest and rational materialist are bounded to eliminate the very
existence of the persons.
Feel free to ask for further precisions, it is a rather subtle (and
fundamental) point. Remember that arithmetic, viewed from inside is
FAR bigger than arithmetic as conceived from pure (extensional) number
theory. A physicalist universe has not that property a priori, and
cannot do those internal epistemological distinctions (except in some
ad hoc ways). This might explain why materialist are often dualist, or
believer in some God (but that is usually an ad hoc completion of the
gap).
Bruno
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David Nyman
> To be short, only intelligible
> ideas exist [only numbers and definable relations exist]. God and matter
> does NOT exist, but they do exist epistemologically. And they are quite
> distinct for what really exist. This does not work for a physicalist,
> because he want to avoid that GOD, and make the global picture a compound of
> the elementary things: he want a universe composed of material stuff, but
> that cannot work if we want maintain the existence (even if epistemological)
> of first person, and that is why honest and rational materialist are bounded
> to eliminate the very existence of the persons.
Yes, this can make sense for me (fortunately we have been round some
of these houses before, so I've had some time to bash my brains into
shape on these points!). I don't wish to fight over vocabulary here,
so when you say "God and matter does NOT exist, but they do exist
epistemologically" I will resist any temptation to accuse you of
contradicting yourself, but rather accept that this statement is a way
of recognising both the reality and the distinctiveness of God,
matter, consciousness and the "intelligible ideas". After all, given
that it's theology we're talking about, I don't find this more
confusing than the doctrine of the Trinity! We agree that "honest and
rational materialist are bounded to eliminate the very existence of
the persons", although (and this is the nub of my argument) to be
consistent they ought at the same time to give up using any vocabulary
predicated on (and entirely derived from) such existence. The problem
is that if they did, they wouldn't have much left to say for
themselves. Perhaps that's why they don't.
>> Consequently, in my view, denial of a distinct first person ontology
>> ought to be seen as having the consequence of radical reduction of the
>> remainder to some such arena of primitives and their relations,
>> independent of any metaphysical postulate of their fundamental nature.
>> Hence, such denial is unintelligible.
>
> Not really, even for a physicalist. Because my point above explain why for
> machine, their consciousness will appear to be both "ontologically real" yet
> quite distinct from anything postulated as primitive in the theory.
I'm still not sure why you would say "not for a physicalist". In
terms of your theory, there is a principled account of why "their
consciousness will appear to be both "ontologically real" yet quite
distinct from anything postulated as primitive in the theory", but in
the physicalist theory (say, the "identity" version) there can be no
such account, given the premise that only the physical primitives are
"really real". Of course, if their theory is physicalism + CTM (which
we both believe to be incorrect), they are equating consciousness =
computation, but the problem with this is that, in the physicalist
theory, "computation" just isn't anything of the sort you describe
above; it's just certain kinds of relations that happen to exist
between entities defined solely in terms of the "real reality". To
make this theory coherent, the physicalist would have to accept that
"computation" additionally has just the kind of "ontological reality"
and distinctness you describe. But then, in the face of physicalism,
this would be, as you remark, frankly dualistic (and also, in this
case, wrong, unless UDA is false).
David
David
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Bruno Marchal
Absolutely.
Except for consciousness, those correspond two the epistemological
distinction between p (truth, God), Bp (intelligible: it splits into
two parts (provable and unprovable) which play a role in the machine
acknowledging her ignorance), Bp & p (the soul, which is when the
intelligible connects with the transcendental: truth), Bp & Dt
(matter, which is when a reality exist: it is weaker than truth,
because it is only the possibility of the (any) truth.
Thoses modalities are extensionally equivalent. for all arithmetical
p, once the ideally correct machine is chosen, we have, with p
sigma_1, that p <-> Bp <-> Bp & p <-> Bp & Dt. yet, the machine cannot
proves those equivalence for all p, and this will introduce, from the
machine's views, those insuperable (epistemological, but real!)
distinctions.
There is a sense to say that from the point of view of God, those
distinction does not occur, but machine embedded in computational
histories (that is: living) are NOT, usually, God. They cannot *talk*
at his place.
Sorry for introducing those arithmetical formal precision, but they
illustrate what you are saying in the case of ideally correct self-
inquiring machines.
> After all, given
> that it's theology we're talking about, I don't find this more
> confusing than the doctrine of the Trinity!
St Augustin's explanation of Trinity is inspired from the three
Plotinian primary hypostases: God (the One), the Intelligible (The
Noùs), and the Soul (the universal or world's soul).
but with mechanism, the Intelligible split (in the provable and
unprovable) and gives the discursive reasoner (man) as a little part
of the noùs. Which gives four hypostases. We get a Quaternity.
And then you recover Plotinus' intelligible matter (Bp & Dt) and
sensible matter (Bp & Dt & p), which both split (in the provable and
unprovable truth).
Which makes a total of 8 hypostases: an Octonity, really :)
Plotinus does not range the matter notion in the primary hypostases,
nor the discursive reasoner. I don't think he would have found
problematic that I call the matter notion "secondary hypostases",
given that he use only "primary hypostase".
> We agree that "honest and
> rational materialist are bounded to eliminate the very existence of
> the persons", although (and this is the nub of my argument) to be
> consistent they ought at the same time to give up using any vocabulary
> predicated on (and entirely derived from) such existence. The problem
> is that if they did, they wouldn't have much left to say for
> themselves.
OK.
> Perhaps that's why they don't.
Making them somehow into contradiction. It is a sort of aristotelian
schizophrenia.
>
>>> Consequently, in my view, denial of a distinct first person ontology
>>> ought to be seen as having the consequence of radical reduction of
>>> the
>>> remainder to some such arena of primitives and their relations,
>>> independent of any metaphysical postulate of their fundamental
>>> nature.
>>> Hence, such denial is unintelligible.
>>
>> Not really, even for a physicalist. Because my point above explain
>> why for
>> machine, their consciousness will appear to be both "ontologically
>> real" yet
>> quite distinct from anything postulated as primitive in the theory.
>
> I'm still not sure why you would say "not for a physicalist". In
> terms of your theory, there is a principled account of why "their
> consciousness will appear to be both "ontologically real" yet quite
> distinct from anything postulated as primitive in the theory", but in
> the physicalist theory (say, the "identity" version) there can be no
> such account, given the premise that only the physical primitives are
> "really real". Of course, if their theory is physicalism + CTM (which
> we both believe to be incorrect), they are equating consciousness =
> computation, but the problem with this is that, in the physicalist
> theory, "computation" just isn't anything of the sort you describe
> above; it's just certain kinds of relations that happen to exist
> between entities defined solely in terms of the "real reality".
Yes. That is why they want that the brain think, not the immaterial
person owning the brain. But a brain does not think more that a
stomach or a tongue can taste a good wine, it is a person who judge
those things. A qualia is real, but it is not defined in term of
neuronal connections, nor of number relations. It is defined in term
of a person (which is not just a machine, really, but a machine
related to truth, or some truth) looking at themselves. Brains and
tongues play only relative roles making it possible for a person (body
and soul) to participate relatively to some probable histories, or
universal entities.
> To
> make this theory coherent, the physicalist would have to accept that
> "computation" additionally has just the kind of "ontological reality"
> and distinctness you describe. But then, in the face of physicalism,
> this would be, as you remark, frankly dualistic (and also, in this
> case, wrong, unless UDA is false).
Unless comp is false, or the UD argument is invalid. Yes.
Bruno
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Stephen P. King
On 01 Oct 2011, at 02:18, David Nyman wrote:
On 30 September 2011 16:55, Bruno Marchal <mar...@ulb.ac.be> wrote:
They are ontologically primitive, in the sense that ontologically they are
the only things which exist. even computations don't exist in that primitive
sense. Computations already exists only relationally. I will keep saying
that computations exists, for pedagogical reasons. For professional
logicians, I make a nuance, which would look like total jargon in this list.
I've been following this discussion, though not commenting (I don't
understand all of it). However, your remark above caught my eye,
because it reminded me of something that came up a while back, about
whether reductive explanations logically entail elimination of
non-primitive entities. I argued that this is their whole point;
Peter Jones disputed it. Your comment (supporting my view, I think)
was that reductionism was necessarily ontologically eliminative,
though of course not epistemologically so.
Yes. This makes sense. Certainly a wise attitude, given that UDA shows that if Mechanism is correct then both consciousness and matter are reduced to number relations. If reduction was elimination, we should conclude that consciousness does not exist (that would be nonsensical for any conscious creature) and that the physical reality does not exist, which does not make much sense either.A physicalist would also be obliged to say that molecules, living organism, etc. don't exist. Note that James Watson seemed to have defended such a strong reductive eliminativism.
But I don't see any problem with reduction, once we agree that some form of existence can be reduced to other, without implying elimination.
Mechanism makes it clear that machine are *correct* when they believe in material form. Indeed all LUMs can see by themselves the rise of matter, or the correct laws of matter by introspection, and they will all see the same laws.
Let me try to be sure that I understand this comment. When you write: "they will all see the same laws" are you referring to those invariant quantities and relations/functions with respect to transformations of reference frames/coordinate systems (which has become the de facto definition of physical laws) or are you referring to our collective human idea of physical laws?
Why does it seem to me that you assume that the physical laws that we observe are the only possible ones? To badly echo Leibniz: How these and not some others? It seems to me that we observe exactly the physical laws that are consistent with our existence as observers within this universe, a universe where we can communicate representations of the contents of our 1p to each other. Communication requires a plurality of possible 1p for each and every separate observer in one universe to act as the template from which signal is distinguished from noise, plurality is insufficient to communications between observers. One needs something like the Hennessy-Milner property for a coherent notion of communication.
There seems to be no a priori reason why we do not experience a universe that contains only a single conscious entity or a universe with completely different laws along with completely different physicality for the observers wherein. IMHO, There is something to the self-selection that Nick Bostrom tedand others have writen about that needs to be included in this discussion in addition to the contraints that communications between many separate entities generates.
Indeed this seemed to me
uncontroversial, in that the whole point of a reductionist program is
to show how all references to compound entities can be replaced by
more primitive ones.
Your remark above seems now to be making a similar point about
arithmetical "reductionism" in the sense that, presumably,
computations can analogously (if loosely) be considered compounds of
arithmetical primitives, a point that had indeed occurred to me at the
time. If so, what interests me is the question that inspired the older
controversy. If the primitives of a given ontology are postulated to
be all that "really" exist, how are we supposed to account for the
apparent "existence" of compound entities?
We need two things. The primitive objects, and the basic laws to which the primitive objects obeys, and which will be responsible of making possible the higher level of organization of those primitive objects, or some higher level appearances of structures.
But why some particular type of primitive rather than some other? It seems to me, for symmetry reasons, that a truly ultimate primitive would have no particular properties associated with it at all! I think that there is a flaw in this reductionist idea, the idea that there exists a fundamental primitive that both is irreducible (by definition!) and has some properties rather than some others. We have been considering some form of Number as our primitive and I have been raising objections to this because while numbers definitely do seem to be irreducible primitives, the very notion that they are numbers vanishes when we consider them at this primitive level because the structure of Arithmetic, which gives meaning and haecceity to them, was dissolved away by the Aqua Regia of Reduction.
One cannot have properties and not the means that generates them, to claim otherwise is a contradiction
In the case of mechanism, we can take as primitive objects the natural numbers: 0, s(0), s(s(0), etc.And, we need only the basic laws of addition and multiplication, together with succession laws:
0 ≠ s(x)s(x) = s(y) -> x = yx+0 = xx+s(y) = s(x+y)x*0=0x*s(y)=(x*y)+x
There is some amount of latitude here. We could consider that there is only one primitive object, 0. Given that we can define 1, 2, 3, by Ex(x= s(0)), Ex(x= s(s(0))), etc.
But that definitive arithmetic structure does not even exist at the level of our one Primitive, 0, therefore we are wrong to claim that our primitive is a number! It is no more a number than a purple and pink polka-dotted Pony! It is the (0, +, *, =) that gives our primitive "number-ness", and it by definition cannot be an ontological primitive because it lacks the necessary multiplicity of extrinsic possible positions that a physical space generates. Just because it is possible to fully express Arithmetic via Goedelian sentences coded as numbers does not require us to believe that the primitive is a number and that that quality of being a number is itself irreducible. Unless there is some form of manifold or non-singular set unto which valuations can be compared and contrasted, each and every number collapses into 0. There is simply no *space* for multiple copies of numbers. "No cloning" follows from "no room to put the clones".
[Or we could take the combinators (K, S, SK, KS, KKK, K(KK), etc.) as primitive, and the combinators laws:
Kxy = xSxyz = xz(yz) ]
It might seems amazing but those axioms are enough to prove the existence of UMs and LUMs, and the whole "Indra Matrix" from which consciousness and physical laws appears at some (different) epistemological levels.
The Indra Matrix (aka Net of Indra) is a *non-well founded* set, it has no true primitives and reductionism goes very wrong in it. Every jewel in the Matrix reflects and is defined by relations to all others. It has no *One* primitive in the well founded sense of a minimal element.
It is the same as the brick in the house example. You need the primitive elements (brick) and some laws which makes them holding together (ciment, gravitation, for example).
The same occur with physicalism. You need elementary particles, and elementary forces which makes them interact. What I show is that IF mechanism is correct, elementary particles and elementary forces are not primitive but arise as the "border of some universal mind" (to be short), which lives, at some epistemological level, in arithmetic.
I agree, physicalist, as a form of material monism is incomplete; but so is any for of idea monism! Only a neutral monism escapes this but at the price of dissolving Everything into Nothing at all. This is why I am motivated to rehabilitate dualism, it solves the incompleteness problems of both material and idea monism and becomes neutral monism in the limit of all possible reductions, thus my proposal is more like dual-aspect monism but not exactly.
If the supposedly
fundamental underlying mechanism is describable (in principle)
entirely at the level of primitives, there would appear to be no need
of any such further entities, and indeed Occam would imply that they
should not be hypothesised.
Yes. And that is indeed why we can say that we explain them. We can explain the DNA structure entirely from the atoms quantum physical laws. So DNA does not need to be taken as a new "elementary" particle. With digital mechanism, atoms and particles are themselves reducible to the non trivial intrinsic unavoidable consequences of addition and multiplication laws.
What needs to be understood about reductionism is that is is showing us that *meaningfulness* itself vanishes at some point in the dissolving. Reduction leads, eventually, to Neutral and Unnameable Monism, not to Number or Arithmetic Realism.
Yet the bald fact remains that this is
not how things appear to us.Why? DNA seems clearly to be explainable by the atoms and their laws, like house seems clearly to be explainable in term of bricks and cement.
At the level of atoms there in no such thing as Van Der Walls forces, for instance, just as there is no such thing as temperature at the level of atoms. So I am skeptical of this claim of explainability. Why? DNA seems clearly to be explainable by the atoms and their laws, like house seems clearly to be explainable in term of bricks and cement. Brick and cement can be used to construct a blue print of the house, but the process of using concrete and bricks to build blueprints is a tiny bit different from building a house of those same brick. There is nothing inherent in a brink that demands that it build a house...
For the reduction of physics to numbers, it might seems less obvious, because we are programmed to take seriously our "epistemological beliefs". A cat would have less chance of surviving in case he doubts the existence of the mouth. So brain have emerged by simplifying the possible world view, but this is due to habitude, and is comparable with many illusion we have had in the past: the sun looks like moving around the earth, but on close inspection, it is the earth rotating on itself, and the move of the sun is a local "illusion". Matter seems to exist in some ontological primitive way, but on closer inspection, it emerges from group symmetries, which themselves emerges from the provable symmetries of the sigma_1 arithmetical sentences when observed by machine.
That very same emergence from symmetries is true for numbers!!!!! THis is shown by how we can identify numbers as the equivalence over a class of arithmetic operations. There is not thing *special* about numbers that allows us to violate the neutrality principle that I mentioned above. You seem to ignore the fact that to be "observed by a machine" is not a purely arithmetic act. Numbers, in themselves, do not act at all. They are static relations. A static relation cannot implement an observation or any other kind of action.
So should such compound appearances be
considered entirely a matter of epistemology?
Yes, but there are many layers of realities available inside arithmetic, and nuances can be introduced. Take the example of prime number, or even of universal numbers. Those can be said, if we want to, as existing as much as the primitive 0, 1, 2, 3, ... After all they are only special numbers.But consciousness and matter are more properly epistemological (first person singular and first person plural respectively). Those are not numbers, but are number experiences, and those, mainly due to our self-multiplication in arithmetic, are related to infinities of arithmetical relations.A notion like a computation, or a computable functions is intermediate, they can have description, which will be numbers, and extension which will be, usually, sequences of numbers.
Layers which reduction dissolves into nothingness. Eventually the very property of being distinguishable dissolves away too and no properties at all are left with which to distinguish 0 from anything else.
IOW, is the
first-person - the "inside" view - in some sense the necessary arena -
and the sole explanation - for the emergence of anything at all beyond
the primitive ontological level?
You don't need a notion of first person to say that prime numbers exist, or that universal numbers exist. Those are just numbers having special property due to the richness of the laws of addition and multiplication when taken together. But UDA shows (I think) that matter and consciousness are first person collective constructs of all the numbers.
Usually, and conventionally I consider that numbers exist primitively even if they have special properties.
*special properties*? How so? Where does the difference between being a number and not being a number remain at the most primitive level?
So I gave the same type of existence to prime numbers, even numbers, or universal numbers. They are captured by sentences with the shape:Ex ( ... x ...), where (... x ...) represent some arithmetical proposition (which contains only the symbols 0, x, y, ..., +, *, s, and the logical symbols).(The proper epistemological existence will be defined by the modal logics like BEx(B(.... x ...), or []<>Ex([]<>(... x ...). The last one are still pure arithmetical formula (thanks to Gödel translation of B in arithmetic), but they have a special "meta-role", and describe what machines can believe, feel, observe, etc.
OK?
Bruno
Idealism is an epic fail, not matter how sophisticated it is, just as materialism fails and for exactly the same reason.
Onward!
Stephen
meekerdb
[SPK]
Let me try to be sure that I understand this comment. When you write: "they will all see the same laws" are you referring to those invariant quantities and relations/functions with respect to transformations of reference frames/coordinate systems (which has become the de facto definition of physical laws) or are you referring to our collective human idea of physical laws?
Why does it seem to me that you assume that the physical laws that we observe are the only possible ones? To badly echo Leibniz: How these and not some others? It seems to me that we observe exactly the physical laws that are consistent with our existence as observers within this universe, a universe where we can communicate representations of the contents of our 1p to each other. Communication requires a plurality of possible 1p for each and every separate observer in one universe to act as the template from which signal is distinguished from noise, plurality is insufficient to communications between observers. One needs something like the Hennessy-Milner property for a coherent notion of communication.
There seems to be no a priori reason why we do not experience a universe that contains only a single conscious entity or a universe with completely different laws along with completely different physicality for the observers wherein. IMHO, There is something to the self-selection that Nick Bostrom tedand others have writen about that needs to be included in this discussion in addition to the contraints that communications between many separate entities generates.
Brent
David Nyman
> [SPK]
> But why some particular type of primitive rather than some other? It
> seems to me, for symmetry reasons, that a truly ultimate primitive would
> have no particular properties associated with it at all! I think that there
> is a flaw in this reductionist idea, the idea that there exists a
> fundamental primitive that both is irreducible (by definition!) and has some
> properties rather than some others. We have been considering some form of
> Number as our primitive and I have been raising objections to this because
> while numbers definitely do seem to be irreducible primitives, the very
> notion that they are numbers vanishes when we consider them at this
> primitive level because the structure of Arithmetic, which gives meaning and
> haecceity to them, was dissolved away by the Aqua Regia of Reduction.
> One cannot have properties and not the means that generates them, to
> claim otherwise is a contradiction
Stephen, I don't know if the following will help (and I don't know
either if Bruno will agree with it), but there are a few intuitions
that have helped me to get intuitively closer to these topics (to the
extent that I can). First, I try not to be too literal-minded about
"number", at least in any of its "local instantiations". Obviously,
if we try to picture ourselves as being in some way literally "made
out of numbers" in any of their ordinary manifestations, it's very
difficult to make any sense of AR. I'm not suggesting that you are
being this literal-minded, by the way. But speaking for myself, I
tend to intuit comp's starting position on "ontology" as something
like: in order to make sense of CTM, assume some "primitive"
analytical-combinatorial principle which is equivalent to arithmetic
in *all relevant respects*. What remains (almost everything!) is then
to discover whether and how, within precisely these limitations, we
can recover what we're ultimately in pursuit of - mind and matter -
also *in all relevant respects*.
It turns out that, to have any hope of doing this, some key
supplementary ideas are in fact required, and the easiest one to lose
sight of, perhaps, is the critical additional assumption (if indeed it
is correct to call it merely an assumption) of the knower - the
"inside view", or "epistemological reality". Now, however one nuances
terms like "ontology" and "epistemology", we cannot but acknowledge
the personal manifestation of the knower - the first person - as some
intimate amalgam of knowing and being. This "amalgam" I take to be an
irreducible fact, but nonetheless what comp seeks to show is how the
"logical ontology" of AR can both underpin (i.e. form the structural
basis of), and permit reference to, such epistemological facts.
This last point - i.e. that of reference - actually seems to me to be
the strongest motivation for a combinatorial approach to the mind-body
conundrum. Try as I might, I have never succeeded in imagining
another ontologically primitive assumption capable of capturing the
fundamental aspects of reference (and particularly self-reference);
and unless the basis of such reference is built into our foundational
assumptions, it seems to me that the possibility of recovering it
"later" (say, from the ramifications of a physicalist theory) is a
stark impossibility.
I hope this may help, or at least may lead to some helpful amplification.
David
Stephen P. King
I do appreciate your attempts to clarify a possible
misunderstanding on my part. I think I do understand Bruno's UDA result
and its ontological implications and admire the ingenuity of the ideas
involved, but it seems that my critique of it is something that I am
inadequately explaining. I see several problems and unanswered
questions. 1) The explanation of how multiple minds, how ever they are
defined in Lobian or whatever terms, can occur such that an appearence
of coherent and concurrent communications occurs is not explained. 2)
How does the result explain the appearance of a single physical universe
such that 1) can occur within it? 3) How does Bruno's result differ from
Berkeley's idealist such that it avoids its epiphenomena problem.
It is true that I am pursuing a different explanatory model and
thus might be accused of nitpicking Bruno's idea simply to score points
for my arguments, but this is not the case. From what I have studied so
far, Bruno's result fits almost completely inside the Stone duality
based model (on the abstract algebra side of the duality) that I am
exploring such that if Bruno's result is falsified then so is my own
idea. The only real difference between Bruno's work and my own (other
than my educational status!) is that Bruno seems to reject the physical
world as having a necessary existence while I do not.
Onward!
Stephen
Bruno Marchal
On 10/3/2011 8:43 AM, Stephen P. King wrote:[SPK]
Let me try to be sure that I understand this comment. When you write: "they will all see the same laws" are you referring to those invariant quantities and relations/functions with respect to transformations of reference frames/coordinate systems (which has become the de facto definition of physical laws) or are you referring to our collective human idea of physical laws?
Why does it seem to me that you assume that the physical laws that we observe are the only possible ones? To badly echo Leibniz: How these and not some others? It seems to me that we observe exactly the physical laws that are consistent with our existence as observers within this universe, a universe where we can communicate representations of the contents of our 1p to each other. Communication requires a plurality of possible 1p for each and every separate observer in one universe to act as the template from which signal is distinguished from noise, plurality is insufficient to communications between observers. One needs something like the Hennessy-Milner property for a coherent notion of communication.
There seems to be no a priori reason why we do not experience a universe that contains only a single conscious entity or a universe with completely different laws along with completely different physicality for the observers wherein. IMHO, There is something to the self-selection that Nick Bostrom tedand others have writen about that needs to be included in this discussion in addition to the contraints that communications between many separate entities generates.
The conservation laws come from the requirement that we want our laws to be the same for everyone at every time and place. This is our idea of "laws". I'm sure you're familiar with Noether's theorem and how she showed that conservation of moment comes from the requirement of invariance under spatial shifts, etc.
My friend Vic Stenger has written a book, "The Comprehesible Cosmos", which shows how this idea extends to general relativity, the standard model, gauge theories, etc. and provides a unified view of physics. I recommend it.
Stephen P. King
--
Hi Brent,
I am taking Noether's theorems into account. Furthermore, you might note that those theorems collapse if there does not exist spatial and/or temporal manifold.
Hi Bruno,
Did you happen to have any comment on the rest of my post? It seems that you are intentionally avoiding my argument.
Onward!
Stephen
meekerdb
The conservation laws come from the requirement that we want our laws to be the same for everyone at every time and place. This is our idea of "laws". I'm sure you're familiar with Noether's theorem and how she showed that conservation of moment comes from the requirement of invariance under spatial shifts, etc.
That is beautiful and rather convincing.
My friend Vic Stenger has written a book, "The Comprehesible Cosmos", which shows how this idea extends to general relativity, the standard model, gauge theories, etc. and provides a unified view of physics. I recommend it.
The part of physics is interesting, but if he would take more seriously the mind-body problem, I think he would appreciated the comp new form of invariance for the physical laws: that is, that the laws of physics do not depend on the initial universal theory. It does not depend on the choice of the computation-coordinates (the phi_i).
Bruno
--
Hi Brent,
I am taking Noether's theorems into account. Furthermore, you might note that those theorems collapse if there does not exist spatial and/or temporal manifold.
Stephen P. King
--Hi,
Yes, gauge theories are built on transformations in an abstract space but if you examine those theories carefully you will find that not only is there some form of continuity and smoothness allowing the construction of analytical solutions, but also there exists a mapping between behaviors in those abstract spaces and observable phenomena. If this later mapping did not exist then the theories could not be claimed to be "physics", at best they would merely be abstract math and might be considered to be just patterns of abstract games played by imaginative entities.
It is mathematics that needs to be careful not to fall into solipsism, for if it has no relation at all with the physical then how does one even consider notions of knowledge of it! Idealism is a very seductive ontological model but it suffers from a very simple but fatal flaw: it reduces all aspects of physicality, such as space, time, solidity, etc. , to mere epiphenomenal descriptions and thus removes any possibility of a coherent notion of causality, time and location. Witness how mathematical entities are claimed to exist independent of physicality, is this not a claim that they have a completely separate existence. How then does one propose the ability to know of the properties of such mathematical entities? If you examine Platonism carefully you will find that it assumes a crude form of substance dualism. Study Plato's writings about "noesis" and the allegory of the cave...
I demand that our explanatory models be observationally falsifiable and self-consistent, thus avoiding the pitfalls of mystisism, but when one is looking into ontological models then one must be careful to have some form of continuance between the ontological aspects of the model and some connection to observability (by many independent observers). My interest in in ontology and cosmogony models, thus my membership to this List. :-)
Onward!
Stephen
Bruno Marchal
On 10/1/2011 9:50 AM, Bruno Marchal wrote:[SPK]
On 01 Oct 2011, at 02:18, David Nyman wrote:
On 30 September 2011 16:55, Bruno Marchal <mar...@ulb.ac.be> wrote:
They are ontologically primitive, in the sense that ontologically they are
the only things which exist. even computations don't exist in that primitive
sense. Computations already exists only relationally. I will keep saying
that computations exists, for pedagogical reasons. For professional
logicians, I make a nuance, which would look like total jargon in this list.
I've been following this discussion, though not commenting (I don't
understand all of it). However, your remark above caught my eye,
because it reminded me of something that came up a while back, about
whether reductive explanations logically entail elimination of
non-primitive entities. I argued that this is their whole point;
Peter Jones disputed it. Your comment (supporting my view, I think)
was that reductionism was necessarily ontologically eliminative,
though of course not epistemologically so.
Yes. This makes sense. Certainly a wise attitude, given that UDA shows that if Mechanism is correct then both consciousness and matter are reduced to number relations. If reduction was elimination, we should conclude that consciousness does not exist (that would be nonsensical for any conscious creature) and that the physical reality does not exist, which does not make much sense either.A physicalist would also be obliged to say that molecules, living organism, etc. don't exist. Note that James Watson seemed to have defended such a strong reductive eliminativism.
But I don't see any problem with reduction, once we agree that some form of existence can be reduced to other, without implying elimination.
Mechanism makes it clear that machine are *correct* when they believe in material form. Indeed all LUMs can see by themselves the rise of matter, or the correct laws of matter by introspection, and they will all see the same laws.
Let me try to be sure that I understand this comment. When you write: "they will all see the same laws" are you referring to those invariant quantities and relations/functions with respect to transformations of reference frames/coordinate systems
(which has become the de facto definition of physical laws) or are you referring to our collective human idea of physical laws?
Why does it seem to me that you assume that the physical laws that we observe are the only possible ones?
To badly echo Leibniz: How these and not some others?
It seems to me that we observe exactly the physical laws that are consistent with our existence as observers within this universe, a universe where we can communicate representations of the contents of our 1p to each other. Communication requires a plurality of possible 1p for each and every separate observer in one universe to act as the template from which signal is distinguished from noise, plurality is insufficient to communications between observers. One needs something like the Hennessy-Milner property for a coherent notion of communication.
There seems to be no a priori reason why we do not experience a universe that contains only a single conscious entity or a universe with completely different laws along with completely different physicality for the observers wherein.
IMHO, There is something to the self-selection that Nick Bostrom tedand others have writen about that needs to be included in this discussion in addition to the contraints that communications between many separate entities generates.
[SPK]
Indeed this seemed to me
uncontroversial, in that the whole point of a reductionist program is
to show how all references to compound entities can be replaced by
more primitive ones.
Your remark above seems now to be making a similar point about
arithmetical "reductionism" in the sense that, presumably,
computations can analogously (if loosely) be considered compounds of
arithmetical primitives, a point that had indeed occurred to me at the
time. If so, what interests me is the question that inspired the older
controversy. If the primitives of a given ontology are postulated to
be all that "really" exist, how are we supposed to account for the
apparent "existence" of compound entities?
We need two things. The primitive objects, and the basic laws to which the primitive objects obeys, and which will be responsible of making possible the higher level of organization of those primitive objects, or some higher level appearances of structures.
But why some particular type of primitive rather than some other?
It seems to me, for symmetry reasons, that a truly ultimate primitive would have no particular properties associated with it at all! I think that there is a flaw in this reductionist idea, the idea that there exists a fundamental primitive that both is irreducible (by definition!) and has some properties rather than some others. We have been considering some form of Number as our primitive and I have been raising objections to this because while numbers definitely do seem to be irreducible primitives, the very notion that they are numbers vanishes when we consider them at this primitive level because the structure of Arithmetic, which gives meaning and haecceity to them, was dissolved away by the Aqua Regia of Reduction.
One cannot have properties and not the means that generates them, to claim otherwise is a contradiction
[SPK]
In the case of mechanism, we can take as primitive objects the natural numbers: 0, s(0), s(s(0), etc.And, we need only the basic laws of addition and multiplication, together with succession laws:
0 ≠ s(x)s(x) = s(y) -> x = yx+0 = xx+s(y) = s(x+y)x*0=0x*s(y)=(x*y)+x
There is some amount of latitude here. We could consider that there is only one primitive object, 0. Given that we can define 1, 2, 3, by Ex(x= s(0)), Ex(x= s(s(0))), etc.
But that definitive arithmetic structure does not even exist at the level of our one Primitive, 0, therefore we are wrong to claim that our primitive is a number!
It is no more a number than a purple and pink polka-dotted Pony!
It is the (0, +, *, =) that gives our primitive "number-ness", and it by definition cannot be an ontological primitive because it lacks the necessary multiplicity of extrinsic possible positions that a physical space generates.
Just because it is possible to fully express Arithmetic via Goedelian sentences coded as numbers does not require us to believe that the primitive is a number and that that quality of being a number is itself irreducible. Unless there is some form of manifold or non-singular set unto which valuations can be compared and contrasted, each and every number collapses into 0. There is simply no *space* for multiple copies of numbers. "No cloning" follows from "no room to put the clones".
[SPK]
[Or we could take the combinators (K, S, SK, KS, KKK, K(KK), etc.) as primitive, and the combinators laws:
Kxy = xSxyz = xz(yz) ]
It might seems amazing but those axioms are enough to prove the existence of UMs and LUMs, and the whole "Indra Matrix" from which consciousness and physical laws appears at some (different) epistemological levels.
The Indra Matrix (aka Net of Indra) is a *non-well founded* set, it has no true primitives and reductionism goes very wrong in it. Every jewel in the Matrix reflects and is defined by relations to all others. It has no *One* primitive in the well founded sense of a minimal element.
[SPK]It is the same as the brick in the house example. You need the primitive elements (brick) and some laws which makes them holding together (ciment, gravitation, for example).
The same occur with physicalism. You need elementary particles, and elementary forces which makes them interact. What I show is that IF mechanism is correct, elementary particles and elementary forces are not primitive but arise as the "border of some universal mind" (to be short), which lives, at some epistemological level, in arithmetic.
I agree, physicalist, as a form of material monism is incomplete;
but so is any for of idea monism! Only a neutral monism escapes this but at the price of dissolving Everything into Nothing at all. This is why I am motivated to rehabilitate dualism, it solves the incompleteness problems of both material and idea monism and becomes neutral monism in the limit of all possible reductions, thus my proposal is more like dual-aspect monism but not exactly.
[SPK]
If the supposedly
fundamental underlying mechanism is describable (in principle)
entirely at the level of primitives, there would appear to be no need
of any such further entities, and indeed Occam would imply that they
should not be hypothesised.
Yes. And that is indeed why we can say that we explain them. We can explain the DNA structure entirely from the atoms quantum physical laws. So DNA does not need to be taken as a new "elementary" particle. With digital mechanism, atoms and particles are themselves reducible to the non trivial intrinsic unavoidable consequences of addition and multiplication laws.
What needs to be understood about reductionism is that is is showing us that *meaningfulness* itself vanishes at some point in the dissolving. Reduction leads, eventually, to Neutral and Unnameable Monism, not to Number or Arithmetic Realism.
[SPK]
Yet the bald fact remains that this is
not how things appear to us.Why? DNA seems clearly to be explainable by the atoms and their laws, like house seems clearly to be explainable in term of bricks and cement.
At the level of atoms there in no such thing as Van Der Walls forces, for instance, just as there is no such thing as temperature at the level of atoms. So I am skeptical of this claim of explainability. Why? DNA seems clearly to be explainable by the atoms and their laws, like house seems clearly to be explainable in term of bricks and cement. Brick and cement can be used to construct a blue print of the house, but the process of using concrete and bricks to build blueprints is a tiny bit different from building a house of those same brick. There is nothing inherent in a brink that demands that it build a house...
[SPK]For the reduction of physics to numbers, it might seems less obvious, because we are programmed to take seriously our "epistemological beliefs". A cat would have less chance of surviving in case he doubts the existence of the mouth. So brain have emerged by simplifying the possible world view, but this is due to habitude, and is comparable with many illusion we have had in the past: the sun looks like moving around the earth, but on close inspection, it is the earth rotating on itself, and the move of the sun is a local "illusion". Matter seems to exist in some ontological primitive way, but on closer inspection, it emerges from group symmetries, which themselves emerges from the provable symmetries of the sigma_1 arithmetical sentences when observed by machine.
That very same emergence from symmetries is true for numbers!!!!! THis is shown by how we can identify numbers as the equivalence over a class of arithmetic operations. There is not thing *special* about numbers that allows us to violate the neutrality principle that I mentioned above. You seem to ignore the fact that to be "observed by a machine" is not a purely arithmetic act. Numbers, in themselves, do not act at all. They are static relations. A static relation cannot implement an observation or any other kind of action.
[SPK]
So should such compound appearances be
considered entirely a matter of epistemology?
Yes, but there are many layers of realities available inside arithmetic, and nuances can be introduced. Take the example of prime number, or even of universal numbers. Those can be said, if we want to, as existing as much as the primitive 0, 1, 2, 3, ... After all they are only special numbers.But consciousness and matter are more properly epistemological (first person singular and first person plural respectively). Those are not numbers, but are number experiences, and those, mainly due to our self-multiplication in arithmetic, are related to infinities of arithmetical relations.A notion like a computation, or a computable functions is intermediate, they can have description, which will be numbers, and extension which will be, usually, sequences of numbers.
Layers which reduction dissolves into nothingness. Eventually the very property of being distinguishable dissolves away too and no properties at all are left with which to distinguish 0 from anything else.
[SPK]
IOW, is the
first-person - the "inside" view - in some sense the necessary arena -
and the sole explanation - for the emergence of anything at all beyond
the primitive ontological level?
You don't need a notion of first person to say that prime numbers exist, or that universal numbers exist. Those are just numbers having special property due to the richness of the laws of addition and multiplication when taken together. But UDA shows (I think) that matter and consciousness are first person collective constructs of all the numbers.
Usually, and conventionally I consider that numbers exist primitively even if they have special properties.
*special properties*? How so?
Where does the difference between being a number and not being a number remain at the most primitive level?
[SPK]So I gave the same type of existence to prime numbers, even numbers, or universal numbers. They are captured by sentences with the shape:Ex ( ... x ...), where (... x ...) represent some arithmetical proposition (which contains only the symbols 0, x, y, ..., +, *, s, and the logical symbols).(The proper epistemological existence will be defined by the modal logics like BEx(B(.... x ...), or []<>Ex([]<>(... x ...). The last one are still pure arithmetical formula (thanks to Gödel translation of B in arithmetic), but they have a special "meta-role", and describe what machines can believe, feel, observe, etc.
OK?
Bruno
Idealism is an epic fail, not matter how sophisticated it is, just as materialism fails and for exactly the same reason.
Onward!
Stephen
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